Latinx - Using "x" works if you only ever use it in text, or if you're doing it for a name like Malcolm X.

If these people care so much about what us Latin Americans think about word usage, then try to make the term "the US" more commonly used than "American". I can tell you that we most definitely care more about that one than some made-up term for Latino, as there is indeed not a single person here that refers to things from the US as "American", since America to us is a continent first and a country second. "American" is used only of there is no possible way to make "USA" or "the US" sound grammatically natural, which is not often.

But naturally, I am arguing with a brick wall here since I am working under the assumption that these people actually care about our opinion, which they do not. We are just a concept – an ideal to them, not actual people with actual opinions.

The Western version of "Latino" that they came up with without asking the opinion of a single actual Latino on its conception.