Even sex isn't fully binary; there are people with other sex chromosome combinations than XX or XY. And people who, due apparently entirely to biology (endocrinology stuff, how their bodies react to hormones etc), develop different sexual characteristics than their XX or XY chromosome combo typically leads to.
So even "there are only two biological sexes" -- while less untrue than "there are only two genders" -- is apparently not an entirely 100% "true biological fact".
Well, as said in the sibling comment, even for clinical sex it's not that simple. Intersex is a fact of life.
As for gender it's a social construct so using a binary qualification makes no sense. One could say it's a spectrum but it doesn't even have to be this restrictive. Why force people to take the whole package of constructs and ethos from either one? What's wrong with having a beard and makeup? Is this insanity to you?
Of course this is not about identifying as object. Please don't use mediocre rhetoric like that.
So even "there are only two biological sexes" -- while less untrue than "there are only two genders" -- is apparently not an entirely 100% "true biological fact".