Are we not considering many Roman customs brutal, awful, and barbaric? What did the Carthaginians not do that the Romans did?

I would consider sacrificing living children to be brutal and grotesque no matter who does it or for what reason, Roman, Carthagian or Aztec, or anyone else. As for your premise, it's flawed. For a society whose world view supposedly stems from Roman culture, we're kept extremely aware by many sources about how brutal the Romans could be too. It's hardly something painted pretty by modern media or books. Quite the opposite.

It's also generally absurd to think that I must automatically be influenced by some propaganda if I consider plausible the ancient records and evidence of another society's extreme sacrificial practices.

As another comment in this reply thread mentions, (though it mistakes Aztecs with Maya), people spent decades thinking that accounts of mass Aztec child sacrifice were colonial era-biased exaggerations, until mass graves of children were much more recently found showing signs not only of sacrifice but torture in advance (to induce tears for the god Tlaloc among other reasons).

Sometimes historical cultures are just awful in certain ways that have to be mentioned in posterity, even if we can appreciate other aspects of those cultures. This applies to any culture and should.