I'm just going to throw out that I know several people working as psychologists and educators in rural Mexico, specifically Michoacán, and quite a few of them have had to learn at least one native language in order to even get by with the locals.
That being said, taking how I interpreted the OP, it seems to be asking if Nahuatl (or any other indigenous language) can remain in official capacity in a European colony IOTL, and if native religion could remain official as well.
As for the linguistic point, as was pointed out, this was the case until 1696 - and not just nominally, either, Nahuatl was being taught to non-native speakers who lived in the colonies simply because it was easier for officials to use a "native" language, but it was taken as impossible to have people proficient in all of them. Even after this point, texts and legal proceedings in Nahuatl were still used in colonial legal systems, albeit often with Spanish translators.
If we're to keep this ongoing, I'd guess three things need to happen. Most obvious is avoiding the OTL ban on all non-Spanish official languages in 1696. Second is probably a geographically smaller New Spain, so that the aforementioned teaching of the language to other native populations remains a viable strategy. Third is the Spanish policy of resettling Nahuatl speakers, especially Tlaxcallans, to other parts of New Spain - make this a bit more extreme (possibly along the lines of how the OTL Incans constantly relocated ethnic groups to discourage rebellion), and you might be able to keep Nahuatl as at least a very powerful second language in Mexico/Central America. Similar policies could probably be applied with either Quechua or Aymara in the Andes.
As for the religion, I don't see that one happening under Spain. It didn't die out officially IOTL, and I can even see it faring better, but I don't imagine it would ever gain official or even semi-official status. Maybe different colonizing countries could give you that result...