I don’t know what the rules were, but I do know people who do.
The Mexican Inquisition was actually a not insignificant part of the Texas revolution, as Protestants and Jews fled Mexico for Texas with promises of religious freedom, which were ultimately proven to be lies.
Having met MWT in real life, he might be best able to expand, given his ancestor was burned at the stake for being Jewish in Mexico.
I don’t have time to read the thread to figure out the dispute here (if there is a dispute), but there were plenty of Jewish immigrants and Conversos in Mexico.
Starting with (probably) Columbus himself. (His mother being purportedly Jewish and he wrote his log in Hebrew.) He even put off the the trip a day because it was Tisha B’Av, which is not a good day to start anything.
Jewish sailors were so common because Jews were not allowed to own real property (generally) and had to earn a living by a trade (e.g., being a sailor) that when the Inquisition got going (in 1492) so many went rogue that there’s a book about it — Jewish Pirates of the Caribbean.
As far as there being an Inquisition in Mexico, yes, there was. Pretty hard to have an Inquistion if no one came, so I guess plenty of Jews were in Mexico.
The humble flour tortilla is, in fact, Jewish, as it was created for Passover. (The largely unlearned Jewish population being uncertain if corn was kosher, due to its status as a deity among the natives.) You can sorta tell where Jewish Mexicans settled by how common the flour tortilla is in that area.
Most notably (to me) is Luis de Carbajal who is an ancestor of mine — and who was burned at the stake for being Jewish in 1596.
Note the rules you mention regarding non-immigration of Jews and first generation converts were ignored for immigration to remote areas of “New Spain” like Nueva Leon (which is now northern Mexico and Texas).
If you need more than this (or sources), please ping.