If you don't want a gendered word, which is very reasonable, "Latin" is perfectly good and has "Latino or Latina" as one of its dictionary definitions.

If you want a brand-new word, Latine is free.

But "Latinx" is an abomination to anyone who loves the Spanish language. I'm very for more inclusive language, but I will never ever say that word.

Also - none of these songs are particularly awful, and all of them were popular over a wide group, including Latins, so I suspect you're projecting your own tastes here.