The objective observation is that there are men that when asked "are you a trans women?" answer yes. That group of men are a distinct sub-group of men.
There are only two reasons that the phrase can be objected to 1) if you think trans women are a sub-group of women or 2) think there are no men who when asked are you a trans women would answer yes.
We have had people argue for 1) but I've never seen anyone argue against 2). So far at least.
I think the issue some people are having with this phrase is that they are loading it with a whole load of baggage about other things. As if they think it is conceding something or it is some sort of trap to wedge something in, when it is merely an objective fact, indeed you don't need objective in that at all, it is simply a fact.
Very true Darat, the observation is that an answer to the affirmative was given; a simple fact. However the original phrase was objective criterion/ia which would be objective evidence that the answers were true. I do note that you were not the first to use the phrase objective observation.