With regard to your question, it works either way so there's no particular ambiguity. But since pronouns usually go to the most recent appropriate person/group, and you had not yet referred to the OP explicitly, the "they" could refer to a subset of native speakers who find it unnatural which also happens to include the OP, or just to the OP given the broader context of the message. And either way your comment comes out meaning the same thing:
People feel what they feel and can't be wrong about what they feel (because it's feeling, not a rational thing).
I don't disagree with that in any way whatsoever. But it doesn't mean that the OP is fundamentally correct either. I find the phrase "he/she" to be awkward, ignoring whether it's inclusive or not (which it isn't). "He" is fundamentally gendered despite what many people want to believe and is even less inclusive (even if we assume only the male and female genders, it necessarily excludes half the population). Consequently, singular "they" ends up being the most natural way to express a non-gendered arbitrary person, especially given that English has an 800+ year tradition of using it in that sense.