OTOH people historically have not been too concerned about candidates' religious details.
Correct. The First Amendment religious protections have two parts: the prohibition of an "established" religion and the "free exercise" clause, which says you're free to practice your religion, not just keep it packed away for private use in Church.
These two parts only come into conflict when one's practice of religion attempts to impose observance requirements on others (which is the main reason why Sharia is incompatible with the U.S. Constitution). So for example, while it's admirable that Chick-Fil-A chooses to not do business on Sunday, mandating that all businesses be closed on Sunday is attempting to impose a religious observance requirement on others, which is why so-called "Blue laws" are unconstitutional.
So this sort of fear-mongering is baseless. Cruz or anyone else is free to hold and practice whatever faith they choose. Moreover, they can freely attempt to persuade others to join them is these beliefs and practices. But others are equally free to ignore such proselytizing and live their lives peaceably however they choose. That's the American way and I'm sure Cruz, as a constitutionalist, would be the first to agree with that.