How is that any different than just saying “Latin” … I’m genuinely trying to think of how this might be pronounced, particularly with an eye towards American regional accents and yeah… it’s not great.

Latine:

- Lah-teen … rhymes white latrine

- Lat-ein-e … normal “lat”, Germanic pronunciation of “ein”, like the number one or Einstein, “e” pronounced either “ee” or “eh”

- Latin-e … latin-ee, rhymes with matinee,

- lat-tine … lah-tine as in the tines of a fork.

Or my favourite

- Latin-e … just “latin” but spelled with a silent “e”.

This is less than ideal… outside of using mispronunciation as a shibboleth, you normally want a group identifying word to be clearly identified and picked up by any possible group members regardless of if they have heard someone speak it. You want such words to be easily used by the people who identify with it, also crucially it’s self-adoption by the group that is being identified that matters… If no one you would call latine likes you calling them latine, or latinx, or Latino or Latina or Latin… you probably should just ask them what they want and call them that instead, that’s just my opinion from over in Australia where this particular identity/word fight appears to have mostly gone unnoticed against our own local issues.

It's a Spanish word (a neologism, of course, used by a small minority of speakers at present), so pronounce it like any other Spanish word:

https://en.wiktionary.org/wiki/latine#Pronunciation_3

Admittedly the question of how to pronounce a Spanish word in English is non-trivial and subsumes the question of how to pronounce Spanish and the question of how to pronounce English ... but apart from that no special case is required for the word "latine"!

Thanks that is helpful. Is this clearly accepted enough to correct native speakers for example when proofing copy?

The correct name for a group of Latino people is Latinos, or Latinas if the whole group are known to be women.