Seeing as the Moon is heavily used for Lunaala alone, there's more chance that Lunaala will be atleast Fairy-type, as Fairy has mystical connections to the Moon.
There is 3 moves involving the moon: Moonlight, Moonblast and Lunar Dance
But it's fair to ignore Lunar Dance given that it's a signature move (as those often simply suite the type of its pokemon for STAB purposes regardless of theme), so there is 2, and yeah they're both Fairy type.
But wouldn't Pokemon designs involving a moon-theme be just as relevant indicators of type association?
We have the already mentioned Cresselia, which is pure Psychic and delibertaley remained so despite everyone expecting it to be retconned to Psy/Fairy at least.
It does have Darkrai as a counterpart, but it's not even remotely as moon-themed besides for the sake of being Cresselias counterpart.
Then we have Lunatone, which is Rock/Psychic. But in this case, the argument that it was dual-type before Fairy and therefore would not have been retconned anyway is legit. (it would still have made sense to keep Psy regardless though considering its Psy-heavy movepool and the whole "it's a levitating rock").
On the Fairy side there is the Clefairy line and that's less direct, given how it is all about being a fairy first and having moon-associations on top of that.
Looking at a list of Pokemon evolving with the Moon Stone isn't much helpful either, since even though there is 2 Fairies (Jigglypuff and Clefairy) that evolve with it, and only one Psychic (
Munna), it's also used for a Normal one (Skitty) and a big family of Poison types (both Nidoran-lines), which go on to gain Ground upon evolution.
Anything else moon related in the franchise I missed?
EDIT:
Another thing.. as far as the move Moonlight goes, if someone wants to argue that it's type specifically indicates strong moon-association of Fairy, while agreeing that Solgaleo will obviously be Fire-type, then it's worth mentioning thatthe counterpart-move, Morning Sun, is not a Fire type move, so that leaves Moonblast...for now.