Latino (or Latina) is fine. The parent poster is talking specifically about the unpronounceable abomination "latinx" with an X ending. I'm Latino and my family hates it, too (but mostly because it's very woke liberal coded, not because they find it racist, as was asserted). But there are plenty of Latinxes who use it, so... shrug.
It’s hard to believe an actual citizen of Mexico would be offended by you referring to their nationality. “Latino” is a term primarily used by people in the US of Latin American ancestry. “Latinx” even more so.
I would recommend simply ignoring anyone who gets offended about how a group they’re not even part of refers to itself.
Yes -- and what ethnic terminology such a person would prefer to use is a complicated and delicate issue, and I think you should call them whatever they want to be called (within reason).
But I certainly wouldn't suggest listening to the opinions of random Anglos who aren't affected by the issue at all claiming that "calling someone Mexican is offensive"
Thats an impossible way to live and get things done. Better to express yourself earnastly, and accept critisim. There is always an opprotunity to learn.