Through the usual meme grapevine I saw a tumblr post on reddit about this. Being gender neutral/genderless in this case is also actively ignoring Spanish linguistics (and arguably culture). Spanish is a gendered language like many others. It's not some patriarchal conspiracy to say Latino instead of Latina or vice versa, it's just how the language works. If I remember correctly as well, the gender neutral form would still be Latino.
Granted, they're being referred to through English here, which one could argue could benefit from just being 'Latin' (confusion between actual Latin aside). I'm of the opinion to keep loan words as close to the original as possible. Language changes over time but some words are still explicitly from elsewhere. So, keep it as Latino/Latina.