Maybe they can relate over cats? America has big cats islam has the smaller cats. Untill they bring a barbery lion.
Kitties are universal.
To be fair, it's mainly the Aztecs (more precisely, the Mexica) whom have a really strong bent towards sun veneration and abhorrence of the night, since their patron god Huitzilopotchli is also their sun god and protector of the world. Otherwise, not every pious person in Mexico would think harshly of Islam's caring for the moon and such, like what Planet of Hats said.
As for fasting, it's practiced in Mesoamerica among religious folks for certain times for many gods, so it's not uncommon, and self-sacrifice (mainly through bloodletting and piercing) is a known concept for peoples like the Maya. It's how the practices are contextualized that makes all the difference. A House of Lamps combined Totonac concepts of purity with Taharah, so such cultural mixing might occur ITTL.
See, this is where I'm trying to walk with care. A House of Lamps and this TL deal in some overlapping magisteria, mainly Muslim settlement of the New World, but I also want to take an approach whereby people will read this and not just say "Oh, he's just copying A House of Lamps." You're likely seeing some differences already. For ex, first contact here was with Brazil, there's been no invasion of the Yucatan, and there are no Aztecs in the Valley of Mexico.
I've tried to divorce myself from soaking up too many other ideas about an Islamic New World for the sake of having the ideas be substantially
my ideas.
Annoyingly, one of the things I have not been able to find is a concise paper or book on specific Tepanec religious practices. We do at least know that Huitzilopochtli in his Aztec form was not an important part of the Nahua religious belief structure until the Aztecs brought him in as their patron deity and restructured the system around him. That said, the Tepanec apparently had an Otomi element to their ethnogenesis considering that the patron god of Azcapotzalco was the fire god Otontecutli, who is also probably called Xocotl but who is also apparently the patron of the Otomi people. This is interesting because the Tepanecs were also apparently Nahua nomads, so some assimilation and cultural mixing must've occurred, possibly in the form of a nomadic Nahua population integrating an already-present Otomi one. Of course, it also seems that Otontecutli may or may not be a variant form of Huitzilopochtli and is probably one of Xiuhtecuhtli-Huehueteotl-combo-god-concept - he is, at least, a warrior-type god associated with fire, the sunset, warriors, metalworking and gemstones. Certainly he seems to be important to the Xocotl Huetzi festival, which involves a bunch of things but also involved the sacrifice of prisoners.
Basically we're in the misty pre-Aztec age on a lot of high Mesoamerican religious practices and we're not
super sure what they were like before the Aztecs came along and put their own spin on the pantheon, and it's even more jumbled because there are a lot of overlapping magisteria and ethnoregional names and traditions around the same broad concepts - e.g. there are probably a dozen Huitzilopochtlis with different names and flavour attributes, and while they may be variants of each other, they are also sufficiently different that the Aztecs had to introduce Huitzilopochtli in detail despite Otontecutli possibly being a form of the same conceptual-based deity. Or maybe Otontecutli was that other fire god.
There are probably some things we're sure of, mind - the Feathered Serpent has been cropping up for centuries, of course, and the Flayed God ain't goin' nowhere.
One thing that does seem evident is that the people in the Valley of Not-Really-Mexico-ITTL are not quite going to be as broadly classifiable as "Oh, the Aztecs" as they might normally be, and that Otomi-speaking people might have a more important role to play, possibly even when compared to Nahua-speakers. Even in Texcoco/Tashquq, the ruling class are speakers of Otomi. OTL, it seems that the Tepanecs eventually gave the Otomi the boot by 1418 and kicked them out of the Valley. At this point, however, the Otomi city-state of Xaltocan still exists. It certainly appears that the Otomi have been there awhile.