So in Spanish you have a word like Oaxaca or México, where the x is in the middle of the word and is pronounced like the h in ha.

When x is at the end of a word its pronounced like k+s.

Or when it is the first letter of a word, its basically an s sound.

So, we get three possible pronunciations rooted in Spanish:

la-tin h (i don't think this really works at all unless you just trail 'tin' with some kind of soft ... consonant only sound?)

la-tinks (arguably this is the most correct pronunciation strictly following the rules of Spanish)

la-tins (works but only if you do not follow Spanish rules for how x is pronounced)

é or e is a vowel pronounced like eh, tbus:

la-tin-EH or la-tin-eh

which is different from latino (OH) and latina (AH).

If latinx and latine are pronounced the same, then that would indicate that a word has been made up which breaks the otherwise quite strict pronunciation rules governing Spanish, introducing an English style 'exception' where this particular word is pronounced this particular way for no apparent reason.

This is a big reason why many (but not all) do not like this term. It either only works when written or to a person familiar with English, who usually pronounce it la - tin - ecks.