Fact: Some roses are red. Opinion: Roses should be red.
Considering that your example of a "fact" starts with an opinion, we don't have much to go off of.
We can get into nuanced comment of fact versus opinion, how facts are mediated through our biases to color our conclusions, or how with many facts we are dealing with statistical models rather than physical laws of the universe, how our biases and collection models can lead us to inaccuracies in what we consider true, or how social truths are only as true as our belief in them, but if we can't even get the difference between fact and opinion, I hold no hope for such nuance.
I agree that men should not win women's beauty contests. That is opinion.
However, trans women are women, not men. This is neither opinion nor fact in the strictest sense, and where nuance gets interesting.
First, you have to understand the difference between sex and gender. Biological sex is not binary, but it's pretty close. Intersex people exist and are often pushed into the binary, though that's changing. Anne Fausto-Sterling asserts that if you add all people who deviate from biological binary sex, you get to about 1.7% of live births. However, there are a lot of ways to compute this number and this would be considered an upper bound. Many of these people are assigned male or female at birth, but it's a factual misunderstanding.
What is interesting here, however, is that even though we could count the number of people who deviate from sex norms, we have trouble identifying who "counts" as intersex. For example, people with Klinefelter syndrome have XXY chromosomes. They are generally counted as male in our system, but we are outside facts now. Do you count a woman as someone with two X chromosomes? If so, this "man" is a "woman."
So even with something as cut and dried as physical sex, we can't get to "facts" because we are working with classifications, and classifications are social constructions and not facts.
Now, we get to the split between biological sex and gender. Gender refers to the role of someone in society. There's no functional reason why we should have two genders in a society, or that they should align with sex. When I say that trans women are women, I am making an argument of social construction, not of "fact."
"Murder is wrong" is a social construction based on a value system, not a fact.
Trans and non-binary genders are speaking to a social construction and role in society rather than a biological sex, but what we do know is that many people do not fit the social constructions of the gender closest to their biological sex.
So, yes, I think a biological male should be able to win a beauty pageant for those in the woman gender. But I want to say that that is opinion based on social construction based on an understanding of the facts of sex and gender. And this is for those who are interested but do not fully understand the difference.
This ignores "overweight" and "ugly", because both of those are social constructions with regard to beauty and is not an interesting conversation to me.
And for consistency, that should go for sports as well of course.
"The Party told you to reject the evidence of your eyes and ears. It was their final, most essential command."
Empiricism, science... they aren't really a tool in your average person's epistemological toolbox. The 99% is as boneheadedly authoritarian today as it was 1000 years ago