I suppose this depends on what you mean by "other religions." Mesoamerica had a plethora of dieties, and groups were constantly swapping, adopting, and adapting each other's gods.
Across Mesoamerica, there appears to be a very broad agreement on religious practice and iconography. This has led some, such a Joralemon, to propose a continuity of deities across time and space. The work of Covarrubias in the mid-20th century in tracing how the imagery of Postclassic gods can find roots in Olmec dieties almost 2000 years earlier reinforces this view.
Certainly, there are dieties in Mesoamerica with a historical depth and geographic spread as to be near universal. Covarrubias put together a famous chart showing the evolution of the Olmec Rain God into Chaac, Cocijo, and Tlaloc among the Maya, Zapotec, and Nahuas, respectively. Likewise, feathered serpent iconography appears to also reach back to the Olmecs, suggesting an antecedent to Quetzalcoatl with that group.
Yet, these are not clear lines of descent, and the three gods named above have their own lines of mythology distinct to those groups: they are not merely the Olmec Rain God copied forward. Among the Aztecs, in particular, the image of Tlaloc is strongly derived from Teotihuacan, not some long forgotten Olmec source. Likewise with Quetzalcoatl, the feathered serpent of the Aztecs seems more derived from Classic Teotihuacano iconography than from tenuous connections to the Olmecs.
Quetzalcoatl would, in fact, undergo a bit of a makeover in the early Postclassic, becoming anthropomophized by the Toltecs into an ideal god-king, and thus a patron of rulers. Yet the Aztecs seemed to have strongly associated Quetzalcoatl with his aspect as Ehecatl, the god of wind, and particularly the wind that swept in before the rain. Quetzalcoatl/Ehecatl thus took on imagery associated with the rich, wet lands of the Gulf Coast, from which the monsoon rains also arrived. The conch shell pendant, Huaxtec cap, and duck-bill mask of Late Postclassic Quetzalcoatl has little in common with the feathered serpent of the Olmecs.
Then there are deities without clear ancient ancestors. Tezcatlipoca was an important Aztec god, perhaps one of the most important, but his connections back to the Olmecs is as dark and distorted as the obsidian mirrors associated with him. Other deities emerge with not even that strong a connection. The "Flayed God" Xipe Totec appears to have emerged from the Tlapanecs in the late Ckassic/early Preclassic. Mixcoatl is a god introduced by the Chichimecs migrating into Mexico from the northern deserts about this same time. Then there are a confused mess of earth-mother goddesses with vague distinctions between them. How separate from Toci is Teteo Innan? What about Tonantzin? Are they actually the same?
This brings us to another part of Nahua religion, which is that a single god rarely was a single god. Instead, major dieties like Teteo Innan or Quetzalcoatl often manifested as various "aspects." So regional differences might distinguish Toci from Tonantzin, but they were recognized as different faces on the same divine force. So too could Quetzalcoatl be Ehecatl, the whole wind, and Tlahuizcalpantecuhtli, the morning star.
To complicate things, Nahua mythology made Quetzalcoatl to simply be one aspect of Tezcatlipoca, the White Tezcatlipoca. Of course, Tezcatlipoca himself was only one aspect of Tezcatlipoca, the Black Tezcatlipoca, and ultimately Tezcatlipoca was only a manifestation of the divine couple Tonacateotl and Tonacacihuatl.
Also, I hope to never again have to type Tezcatlipoca that many times in a row again. Tezcatlipoca, Tezcatlipoca, Tezcatlipoca, Tezcatlipoca. There, done.
The point of all this is that the Aztec pantheon was broad and inclusive, particularly once we consider that the Aztecs were actually three different people. The Mexica, who became the dominant partner in the Triple Alliance, brought their own patron god, Huitzilopochtli.
Patron deities were a thing in Mesoamerica, and sometimes could end up associated with a more prevalent god, and thus becoming another aspect of that deity. The patron god of one of the constituent parts of Chalco appears to have been something like this, being identified specifically as the Red Tezcatlipoca, which was another name for Xipe Totec, but seemingly distinct from both.
The Mexica's patron, Huitzilopochtli, evolved along a different route. As they became more dominant in their local area, Huitzilopochtli started to assume the roles of other gods, so that they became aspects of him. In particular, the lines between Huitzilopochtli and Tonatiuh, the Sun, and fire gods like Xiuhtecuhli and Huehueteotl become blurred.
So, to finally get around to your question, the Aztecs didn't much care what god you worshipped. When conquering a city, they would remove idols from the main temple of their conquest, to be stored back at Tenochtitlan in a special temple for looted idols. This was an action of subjugation though, not conversion.
The Aztecs, rather than forcing "Huitzilopochtlism" on conquered tributaries were far more likely to integrate a new deity into their pantheon. Perhaps the new deity would be adopted as an aspect of an already prominent god. The integration was aided by the already widespread commonality among religions in Mesoamerica, which meant this differences were more about praxis and emphasis than theological schisms.
Diehl 2005 The Olmecs: America's First Civilization
Markham & Markham 1992 The Flayed God: The Mesoamerican Mythological Tradition
Nicholson “Religion in Pre-Hispanic Central Mexico” in Handbook of Middle American Indians, Vol. 10 and 11