Fair enough. Would your position change if she was a real trans?

I didn't state a position....but if you mean my implied contention that you're wrong in your implied contention that it's inaccurate to think trans people are normal, then no it wouldn't change it. Trans people are no less normal than, say, people with green eyes. Very uncommon, but perfectly normal. Which obviously means that no, I don't think it's "weird" to think that trans people are normal - again, any more than it's weird to think that someone who has green eyes is normal.

If you're asking whether it would change my thoughts on a person competing in athletic events that are segregated in to men's and women's sports, that's far more complicated. I'm not sure how I would come down on that - I'm genuinely conflicted, and I think there's compelling arguments on both sides. I don't dismiss the claim that the separation of sports into men's and women's competitions is based on biological sex and not gender - the reason we have separate competitions is in recognition of the biological differences in anatomy that accompany biological sex, and not the social construct that is gender. On the other hand, since we're using "men" and "women" as the divider - and not actually a biological test - it's valid for trans women to argue that they are "women," and thus meet the qualifying standard of participating in that competition.

I don't know how to resolve it, because elite sports almost always involves athletes that have advantageous genetic make-ups competing against athletes that lack those genetic advantages. It's never an "equal" playing field that solely measures who worked the hardest or trained the best - when everyone's working very hard and training very well, the winner is often the person who simply has the best-suited physiology for the competition. It's always an "unfair" competition for the athletes who don't have the optimal biology for the event (leaving aside certain ones where that might not be especially relevant, like the equestrian events). Sex-based divisions are a very crude effort to adjust this broadly - and they are imperfect. I do not know how to solve those imperfections.