I used to work at a Chinese restaurant an the number of people who came in there blithely asking me if we "really" cooked and served cats was astounding.
I got tired of answering the question so often that towards the end I gave up and my standard response was, "No, we only cook and serve idiots who go around saying we cook cats."
I think the very low percentage of lost business was worth it. And this only because my boss told me that this kind of thing did not meet the criteria wherein I was allowed to roundhouse kick patrons in the teeth. If you're going to be a dumbass, at least try to be original.
Because racism is learned. It's the same tired tropes they heard from their parents. Today's racists are racist against Central American and Caribbean immigrants. Twenty years ago it was the Middle East. In the 1970s it was southeast Asians. Before that were... everybody else. This is America. There's always some new cultural group to demonize.
Dehumanising people makes it easy to hate and persecute them, and to blame them for a bunch of stuff which isn't their fault. It really is a classic move with a rich history.
This is funny as the Vietnamese joke about Chinese this way, they have a saying that translates as, 'the only thing they don't eat with 4 legs is a table'
Nothing to do with pets, but in Korea there are places that serve dog. At least it was the case when I was there 20+ years ago. But, of course they're not pets, they're farmed like any other livestock I would expect, and these places were not exactly commonplace even then, so maybe now they're just not a thing? I've not really looked into it.
Now, saying "x" people eat pets is likely just what others have said, a slur used against whichever subset of people is the target of the month. Maybe it once had roots in facts like those I've mentioned, but they're far removed from them now.
Your question is confusing, but I think the answer is...
Racist people heard something. Racist people think it's a fact. Racist people extrapolate from that thing they heard and assume the extrapolation is also a fact.
Cats are/were eaten in Vietnam. I have no idea about Haiti and it's impossible to search it currently. So, this is people jumping to conclusions that immigrants are eating pets.
As you should expect, the truth is actually between the extremes of “facist trope that is completely false” and “all immigrants are evil.” A person in Ohio recently killed and ate a cat, but was not an immigrant.
For anyone who doesn’t want to click the link, it contains bodycam video of a police officer in Ohio recently arresting a US citizen with blood all over her, fur in her teeth, a dead cat nearby, and multiple eye witnesses saying she killed and ate the cat.