The answer probably depends on what you currently have in access. If it's just persons and families, it is not that difficult to find a way to export those to a program like Gramps, which has a nice CSV import, and use GEDCOM if you later want to change to another program. The Gramps CSV format is well defined and can also be expanded if you wish.
If you have tables that contain detailed information from sources that are more difficult to convert, I suggest that you first export your data to a format that is human readable, like CSV, or portable like SQLite, so that you can explore what you have with modern tools. I recommend SQLite because it is supported on platforms like Windows, Linux, even Android, and it gives you a chance to save your own design, and wait for standards to evolve in a direction that supports the way you like to work.
For what is worth, SQLite is also used in RootsMagic, so if you know what to do, you can probably hack that too.