Civil Registration was around in Mexico from 1859 and enforced pretty well from 1867 onwards. The couple could therefore have registered their marriage legally outside the Catholic church.
Actually, post-1917 there should be a civil record to make the marriage legal, as described in the above link:
With the separation of church and state in Mexico, formalized by the 1917 constitution, civil authorities determined that for couples to be legally married they had to be married by the state. Because of the close affinity of the Catholic Church and the state authorities, this rule was not always followed, and church weddings were accepted by the state. Normally, however, couples were married by civil authorities prior to a church wedding. On rare occasions they were married civilly after a church wedding.
Equally, births and deaths around this time should have been registered with the authorities. There may be both civil and church records relating to the same event (e.g. a birth and subsequent baptism).
As a matter of fact many of these these records are up on familysearch although often not indexed; here is a direct link to Ciudad de México/Mexico City.