Moore? Openly hostile to Star Trek? The lifelong classic Star Trek fan?
None of these people are hostile to Star Trek — not Moore’s generation, and not Kurtzman’s. They may take different approaches, they may try to do it better, as they see it (and that’s their job, as writers!), but “They hate Star Trek!” — and the frequent corollary “They’ve been *quoted* as hating Star Trek, I’ve definitely seen that somewhere!” — are fanrage nonsense.
Here's the thing: We all have different priorities and expectations where Trek is concerned, so wanting to make the kinda Trek you, as a fan, always wanted to see is not the same thing as "hating" Trek.
And, honestly, there's no point in doing a new Trek show if you're not going to at least try to put a new spin on it. Now, how far you can tamper with the recipe before you lose more than you gain is always going to be a judgment call, which people of good will can debate, but, again, that doesn't mean you "hate" or "have never watched" the previous versions; it can just mean "we've already done X, so let's trying doing Y this time around."
And critiquing the previous versions, to see what might be improved the next time around, is not being "hostile" to the previous versions. Hell, that's just how things works, as far back as TNG giving Roddenberry a chance to second-guess some of his choices on TOS.
Heck, in his book,
The World of Star Trek, David Gerrold devotes several pages to analyzing TOS's strengths and weaknesses, while suggesting ways to remedy the latter in any future versions of Trek. (Like not always sending the captain on dangerous Away Missions.)
Does this mean Gerrold "hated" TOS just because he wanted TNG avoid certain traps that TOS fell into?
Of course not.