The claim here is that animal cruelty is a part of a particular culture and is therefore justified as a part of preserving the culture. It's basically three bad arguments rolled together:
Cultures change. It once was a sign of status as to how many slaves one owned. That was not worth holding onto for its own sake. It was once part of Aztec culture to decapitate people at the top of temples. Do you really want "culture" to be the excuse for anything? Can someone just claim "suicide bombing is just culture; it's just another form of communication. You're saying "I really don't like your style", just with explosives instead of words"? This is cherry-picking what aspects of "culture" one is willing to preserve as a part of forcing suffering onto sentient beings. If it doesn't work for female genital mutilation, murder, slavery, or dog fighting, then it shouldn't work for any other form of carnism.
If you don't think it matters that carnism hurts animals, well it hurts other people too. So is there any significant difference to me justifying nuking a country because it is part of some imagined "American Culture" of guns and reckless sovereign nation invasion? If it doesn't work there, then why does it work for starving other countries of their resources just so you can have your "culture"? You're still externalizing the costs on other people.