A few thoughts ....

There is a need for nation states to have an appropriate immigration policy ... but the "They are eating Cat and Dogs" is not that, but instead is an attempt to tap into an unfounded fear, and is literally an attempt by a rather rich guy to manipulate people into supporting him.

Yes there are indeed nations where (much to our horror) dogs are on the menu. The example you cite was a guy asking permission. He did not steal your dogs. When asked he gave an honest answer.

The essence of a good lie is that it sounds credible to the target audience.

The rather jaw-dropping twist to all this is that there was an agreed bipartisan border deal a few months ago, the toughest ever seen, and then Trump directed the Republicans to withdraw and not support it so that he could then campaign like this.

Meanwhile over in Springfield, Ohio, the Hatians did not suddenly pop up, they arrived in 2018 - hint : who was president then. If Trump takes issue with them being there, then perhaps he should go have a word with that guy.

Springfield was a town in decline because jobs had been exported to cheaper markets by some rather rich folks who wanted to be even richer. They used to manufacture farm machinery and trucks, but went into decline when that all moved offshore (half the manufacturing jobs were lost between 2000 and 2010).

Then the Haitians arrived and helped to revive things and they experienced an economic upswing.

The rhetoric Republicans are using now, supposedly in support of the residents of Springfield, Ohio, now threatens to completely unravel the economic upswing they had been experiencing.

Even now we have JD Vance doubling down on the xenophobia mythology, and then when cornered, admits that he makes this stuff up.

For more insights, check out NBC : https://www.nbcnews.com/news/us-news/baseless-rumors-haitian-immigrants-threaten-unravel-springfield-ohio-rcna170513