Latin would be ungendered, but it's been said for years by all sorts of people so it doesn't serve the cultural signalling purposes to show that you're enlightened. Gotta use that x to demonstrate your tribal allegiance.

Latin also doesn't imply "of south or central America" in the way latino/latina/latinx/latiné (which is the other approach that's gender neutral and easier to pronounce that I've seen) do. Latin implies, at least to me central European, old and vaguely Italian, as opposed to Latino.

You could also use "Latin American", which may also work, but historically Latino/a have been preferred, possibly since "Latino" is a lot easier to say than "Latinoamericano".

The question is, preferred by whom? Most Hispanic people use "Hispanic", and almost all of the remainder use "Latino". The other terms are fashion statements to show that the speaker keeps up with new intellectual trends, so they lose preference whenever they become too well known; you can date groups like fossil records by seeing whether their name uses "Latinx", "Latina/o", "Latin@", or "Latin".

Or the already widely adopted Hispanic.

Hispanic means Spanish speaking. Spain is Hispanic but not Latin. Brazil is Latin but not Hispanic.