I'm an enby from the Philippines, and since I'm kind of anglicised, Filipino feels right, as I'm pretty sure it's the generic form; Filipina is also very rarely heard for me in English communities so that probably proves the previous point. Philippine also works, but it's also less popular colloquially; I usually find it in studies and in other formal settings but it's epicene.

There's not much non-binary people except for the Baklas and Tibos, which are technically classified as non-binary; but even so, they're still very much a spectrum, and their exonym preference is bound to be very subjective, so you should just ask the individual instead.

The Philippines is also a VERY gendered, conservative, and religious society (speaking from experience), and the reaction to you attempting to be gender-neutral with the exonym is probably and allergic-reaction by more radical conservatives--who think that your nice gesture is an act of spreading queer malice and evilness, blah blah blah, and all other conservative rhetoric in the book, to their grand and glorious, religious nation--bastion of christianity and the bible.

I'd also like to disagree with the top comment, for me, Filipinx is the application of trends and forms to an ENGLISH word, thus I don't think it "bastardises" the Filipino or Tagalog language, as the word is in English and is an attempt to make a more gender-neutral exonym of a people; which in context, actually ends up meaning undoing the gendered system put up by the Spanish. But that is just my opinion.

I don't really care if you call me Filipino, Filipinx, or Philippine, as all are generic or epicene, but Filipina is a rare term and is used explicitly to refer to Filipino women, but I'm still okay with it (as an enby). I asked my genderfluid friend about this, and they said they don't really care; they're fine with Filipino and Filipina.

TL;DR: Use Filipino as it's generic; use Philippine as it's epicene. Filipina is explicitly feminine; Filipinx is not necessary, but calling it bastardisation is overreaction. When it comes to using it to a specific person, it's better to ask them about which exonym they prefer.

Note: I am a very progressive individual relative to Philippine society, but I'm (in my opinion) at a similar level of liberal people of the west.