Perhaps in scope the Aztecs were distinct from prior and contemporary groups, but they were drawing upon millennia of tradition with regards to sacrifice of others and auto-sacrifice. It is important to remember that the Mexica, and the other Nahua groups generally, were relative late-comers to the mainstream of Mesoamerican history, with the bulk of their migrations from the northern Chichimeca into central Mexico taking place in the Postclassic period. As a result, they had a wealth of prior cultures and traditions to adopt and adapt.

The stereotypical heart removal practice, for instance, has clear antecedents going all the way back to the Classic Maya, who also practiced a suite of other forms of sacrifice such as decapitation or being shot with arrows, the former of which was often associated with ritual ballgames. Likewise, the practice of flaying the skin and wearing it is associated with Xipe Totec, whose ritual complex was widespread throughout Mesoamerican by the Postclassic, has much earlier origins in present day Oaxaca and Guerrero. It is also in the Valley of Oaxaca that we get dramatic representations of the sacrifice of enemies with the Dazantes at San Jose Mogote, which date to the mid/late Preclassic. If we go even further back in time, there is some evidence of Olmec human sacrifice, in the form of what appears to be a decapitated head on a stela at Tres Zapotes, and even child sacrifice has been hinted at by infant bones found at the El Manati offering site.

So no, none of what the Aztecs were doing was particularly new. Human sacrifice has a long pedigree in Mesoamerica, even if the particular function and meaning of the practices changed between societies and over time. Carrasco, in City of Sacrifice makes the point that what distinguished the Aztecs was the scale of the practice, but that this was incorporated into their mythology at the very beginning:

We see that the question of the increment in human sacrifice is partially answered through the discovery of within the myth that Huitzilopochtli kills not just one goddess, but he annihilates many beings -- his sacrificial aggression extends to the killing of almost all the divine beings. This significant discovery appears to be Aztec-specific; that is, the mythic structure of massive sacrifices seems to be particularly Aztec.

In other words, the scale of sacrifices practiced by the Aztecs was distinct from past practices, but Carrasco feels this is something baked into the origin myths of the Mexica themselves. A writer less focused on symbolism and more on the realpolitik of Mesoamerica, such as Hassig, might not interpret the practice differently, however, pointing more towards the effect of weakening and intimidating political opponents, while simultaneously providing a very visible display by a ruler of his military prowess. These views are not necessarily in opposition, but instead point towards the multifactorial explanations for the increase in the scale of sacrifice we see with the Aztecs.

As for the other members of the Triple Alliance, by the later Imperial period, Tlacopan is treated more like an appendage of the Mexica than an independent state. There's no reason to think they had some sort of religious division. There is a literary tradition of portraying Nezahualcoyotl, the great Acolhua ruler, as having reservations about human sacrifice, or even outright rejecting it. This stems from writings by Alva Ixtlilxochitl in the 17th century wherein the author, a devout Christian, is seen as trying to not only clean up the "pagan" associations of his ancestor, but also depict him as practicing a sort of proto-Christian form of monotheism. This protray is not taken seriously, in part because writings contemporary with, and earlier than, Alva Ixtlilxochitl seem to have no problem in showing Nezahualcoyotl as an enthusiastic participant in the state sacrificial rituals. Nezahualcoyotl, who grew up living with the ruling dynasty of Tenochtitlan, was also responsible for building a very large Mexica style temple to Huitzilopochtli and Tlaloc to Texcoco, something that would be very unusual for someone supposed rejecting that religious practice.