An attribute that can change based on someone's feelings is definitely not objective. And all of the genders that are neither male nor female were invented in the last few decades, so membership in one can't be factual. Likewise, membership in a construct called "gender" which is divorced from biological sex was also invented within the last century, so that can't be said to be factual either.
Objective [1]:
1. Of or relating to a material object, actual existence or reality.
2. Not influenced by the emotions or prejudices.
3. Based on observed facts; without subjective assessment.
Fact [2]:
1. Something actual as opposed to invented.
2. Something which is real.