I have recently been to a family reunion in which we all offer updates to our branch of the family, such as births, deaths, graduations, etc. Therefore personal data about me, my kids and my parents is shared to a much broader group of relatives - hundreds of them - many of whom I do not know. I recently saw someone who is a member of the Church of Jesus Christ of Latter Day Saints, that I do not know, post questions about my great-grandmother on facebook asking for her death dates and burial location. Another member of the family then scanned and posted the family group sheet onto facebook. It is a closed group, but I still felt strange about what might happen to this information.
Why does the LDS church search for genealogy records?
What do they do with the information (besides store it and make it available to genealogy researchers)? i.e. what is the religious use of this data?
If I have a member of the LDS church in my family, is it inevitable that they will perform a 'baptism for the dead' ritual for me, my kids, my parents, grandparents, etc. once we die?
PLEASE NOTE: I am not a recluse or a luddite. I am not interested in hoarding or hiding my data away, or ceasing my own hobby/interest in genealogy research, but I am concerned about religious activities performed in my or my loved one's names that we are unaware of. Therefore I am seeking clarification on the above questions. Thanks.
Members of the LDS church are not as homogeneous as they would like to be, so even the official policies of why they do things, and what they will do with information is open to some interpretation even within their own membership, whether the official policies are written to allow for this or written specifically to prevent such 'interpretation'. There are in fact 'checks' in place to attempt to either prevent or 'fix' any individual going beyond the bounds of the intent of the framers of these policies, and both the number of and the 'teeth' of these 'checks' have increased in recent years, but that detail is beyond the scope of this question.
That said, @Brian's answer is pretty reasonable for the majority of people doing this sort of thing. I can give a little more detail.
When individuals do it, it can be for religious reasons, or any other reasons that any other genealogist performs research (curiosity, record keeping, feeling connected/dispelling loneliness, trying to be royal/famous, bragging about numbers, fitting in with others who research), and those religious reasons can be multifaceted too (earnest belief that they are helping people, doing because their religion/church says so, trying to 'earn points' on a supernatural scoreboard [not official doctrine, but happens none the less]). The reason this matters is because of what happens next.
Those who are collecting points or bragging about numbers will likely be unscrupulous about what they do with the information, and may even use it against the wishes of the individual's family. Pretending otherwise suggests that there could possibly be an organization of millions that doesn't have 'ding-dongs', which is absurd, even and especially if one takes its claim of being supernaturally appointed as fact. On the other hand, most LDSs, in my experience will try, in many cases, to see the names as individuals, and treat them as such, as best they know how. As you know, there are people that think that forcing people to do something 'for their own good' is reasonable, and will think that the rules don't apply to them if the cause is 'just'. But, in general, the information is only used for 'sealing' one's own family together, not, for example, baptizing holocaust victims or famous people.
Regardless of whose information is used, here is what actually can be done with it:
It is put into the database by the individual collector. I believe that current policy is that all data within the database is accessible/searchable to anyone with an internet connection, LDS or not, but requires a free account. Not 100% sure on this, but it is likely that, even if not everyone can get an account, I bet you that your friendly neighborhood mormon would be happy to log in and have you sit at their computer. Even the young missionaries are trained how to help people do this (training quality may vary).
The information can then be formatted to be 'submitted to the temple', which means that the person's information is being prepared for their vicarious proxy baptism or any other religious rites (sealing, etc.). This is not, in anyone's mind, believer or not, a binding action, nor even an efficacious one. Until recently, all this meant was putting the information in order so it could be printed on a pink or blue index card in a human readable order. It could still be printed from the new tool, but is usually sent electronically, and regardless some 'checks' will be run at this step. First it checks if someone else has already 'submitted' this individual, but it also checks if there is an actual measurable relation between the submitter and the individual, as well as looking for other (likely) family members that may be closer in relation. If the system thinks there may be such, it errors out, saying that this submission is (likely) unauthorized. Now, frankly, it isn't that hard to get past this error, for someone who knows what they are doing, but it is a hassle at best, and serves as the most effective barrier against some random LDS trying to baptize grandma without me knowing.
'Taking the name to the temple'. This nomenclature remains from when the colored cards used to be printed on paper from home. This is the next step, after 'submitting'. Religiously, LDS really believe statements attributed to God in Matthew and Malachi in the Christian Bible, and think that everyone, even those who are already dead, deserve to participate in the baptism and 'turning of the hearts'/'binding' mentioned therein. Practically, this means actually doing something in the name of the deceased. This 'something' isn't physically/emotionally intensive (septuagenarians and teenagers perform much of this), is usually between a few minutes to a few hours for each step, and is currently done usually in 4 separate 'stages'. The content of these stages can be researched by following comments in the question, as well as LDS official publications, and elsewhere, but is well outside the scope of GenealogySE. The reason this matters is because of timeline. What actually happens once the deceased individuals' names are 'taken to the temple' is that the submitter will either attempt to perform all the various 'stages' themselves, or place the information into a 'pool of names' from which those who come to the temple for personal spiritual reasons may choose so that they will be able to serve another individual while there. It is rare to even know the submitter, let alone anything about the deceased individual themselves, when this takes place. When a deceased individual's information is put in this pool, the stages will take between months and years to complete. I do not have specific information on current or historical ratios of how many temple visitors bring their own information about deceased individuals for their visit, but I think it likely that the vast majority of visitors use the 'pool'. When the submitter attempts to perform all stages on their own, it could theoretically take less than a day, but in practice only one stage is completed each day. Also, please keep in mind that submitters generally submit groups of names at once, and rarely only one or a pair at a time. In practice this means that the time between entry into the LDS church database and actual temple activity under that person's name will be weeks at a minimum, and often a decade.
How to use this information: If someone were concerned that their family members' information were being used without family permission, by someone with some technical knowledge, sufficiently religiously educated to know the details behind the process I just described, and having the desire to use this information in a manner against the wishes of the religious organization to which they belong (not trying to be sarcastic, these people do exist, just may not be very common), generally that concerned person has two steps to take: First, create a free account (or use someone else's) to monitor whether their own family is actually in the church's database. It is a huge database, some part of their family probably is, but the recently deceased person(s) may not even be there yet. A concerned person would then decide on their own whether to add that information or not. The next step, once the individual's information is actually in the database, it is easy to contact a helpdesk, which deals with requests of exclusion from temple submission as one of their standard duties. Their contact information can be found at https://familysearch.org/ask/help, and currently phone is their preferred method of communication.
So, to answer point 3 above, "Is it inevitable?" Depends on who you talk to. :) Without getting too deep into religious doctrine, many LDS would say yes, but probably not in your case until after Jesus Christ appears physically and publicly to millions, and maybe not for hundreds of years after that. A cynic might say yes, but for the reason that the above mentioned 'ding-dongs' will always exist, and you can't (shouldn't? you have more important things to do, probably) monitor a family history website weekly. In those cases, the people you talk to at the helpdesk are generally practical about such things, and may have suggestions. And though I can't speak to your specific case, I would assume that the facebook requester was gathering information with that being one of their goals, but a polite request to the helpdesk could easily leave the 'no submit' notation on your great-grandmother's information... unless that facebook requester somehow has an equal or better claim on family relationship. They probably don't, it is probably their great great aunt or something, and they are just trying to get their great great grandparent's kids' information complete.
Now, if I may get a little off topic here: Even in a closed group, I think it was highly inappropriate for your family member to post private information about you or your children on a social media website. Sure, they could probably get it other ways if they were a committed stalker, but this is one of the reasons that recent census information is not public, for example. If I were to receive personal information about living people (especially children) that I didn't know and had little to no relationship to, I would feel uncomfortable, but wouldn't really know what to do. The facebook requester, put in the same situation, may or may not have recorded your children's information, and maybe only for the reason that they didn't know what else to do with it. The current LDS suggestion for record keeping is to use their tool to store data in the cloud (and in my mind, cloud is best and most secure for genealogical data anyway, no matter religious persuasion), so it is possible that your information is found there. If I recall correctly, the information of living persons is not visible outside of the person's account who entered it, but I am not completely sure. If I were you, I might strike up a facebook conversation with this requester, and ask them to not record/remove your children's information from their database. You could also find out from them their relationship to your great-grandmother (that is fun anyway), and it wouldn't be unheard of to simply ask what they plan on doing with your great-grandmother's information. If you can't, that conversation doesn't go well (maybe you found the ding-dong?), or you are really very concerned about this, you can also call the helpdesk, who certainly would see the removal of children's names from their database that were added without authorization from parents to be a reasonable request.
The short answer is that LDS ordinances performed for deceased individuals have, at their core, a desire to link families for "all time and eternity". Their belief is that this can only be accomplished by:
accurately identifying individuals and their relationship to each other
sealing these individuals to one another by one holding the authority to do so and
IMPORTANT THING HERE having those ordinances accepted by those individuals who have passed on.
The doctrine is that nothing is ever forced onto anyone ever; the opportunity is just presented, accept it or don't.
As to the "nuts and bolts" the Mormons will do whatever they wish with information gathered from "public" sources.
You decide what "public" means and then decide if it matters to you what is done with it.