Hey! I have done some research on this topic and would like to give my opinion.

 
Let's take trans women as a first example since bigots usually have the most issues with them. For this scenario I'm going to be talking about trans women who are on feminizing HRT (hormone replacement therapy) and thus are 'transitioning', later I would like to add my opinion on 'non-transitioning' trans women.
The most common prescription of hormones for trans women are: estrogen (almost always the case, it's a global standard) and a testosterone suppressor, but the exact medication can differ by your location: in the US spironolactone is most common, however in Europe, Canada and Australia cyproterone acetate is most used. Essentially what these hormones do, is increase the amount of estrogen in your blood and lower (or stop with some medications) the testosterone production. This is important, since the exact hormones in your body are a huge contributing factor to your physical endurance and capabilities. I'd like to add that, in most cases, after prolonged duration of hormone therapy, the hormone levels of a trans woman end up quite similar to those of a cis woman.
According to an article published by the British Journal of Sports Medicine, transgender women have a comparable fitness to those of cis women. It is however very hard to draw an exact conclusion, since there are so many factors to consider when saying: 'physical fitness' and many specifics on a woman's transition can be important to your results. 
So, without elaborating too much, hormone replacement therapy has a huge impact on your general fitness and it can thus be said that a trans woman's fitness is not that different than that of a cis woman!
In addition, you might wonder about the literal physical skeleton of a trans woman and how that might effect things. Well, men are on average taller than women, so if a trans woman has gone through puberty and has therefore developed an adult skeletal frame, yes, they might be taller and have better grip strength. However, if you simply adjust the data for someone's height and weight, these 'advantages' have a significantly small impact on their performance. So again, little difference.

Now, how about trans men? Same story. Their prescription is usually only testosterone, since it's a dominant hormone and acts as it's own estrogen blocker. As stated in an article published by the National Library of Medicine: ''Existing studies in nonathletic trans men have shown that increases in muscle mass and strength occur with testosterone therapy, and physical performance appears to be no different to cisgender men by 1 to 3 years after GAHT.'' 

So, now for my opinion. I'd say just include weight/height categories for certain sports, where needed (which is pretty much already a thing). Non-transitioned trans-women? Well, then I agree that it would be unwise to include them in PROFESSIONAL women's sports, because of 'fairness' and all that. But what I personally think is absolutely crazy, is to exclude trans women or trans men from NON-PROFESSIONAL sports categories that correspond to their gender. Seriously, how hard is it to make an exception for a handful of trans women? Trans people make up such a small percentage of people, it's crazy how obsessed cis people and bigots are with their genitals. 

Just one last thing: true 'fairness' and 'equal chances' don't exist in sports. There are many cis women who have higher testosterone levels than average and simply get lucky with their genes! To exclude trans women from their sport is just one small slip up away from excluding cis women from their sport. Just like with all that bs about bathrooms. Intersex people exist and gender non-conforming men and women exist as well. If we make separate bathrooms for trans people, just wait till they start kicking out taller or gender non-conforming women that 'look trans'. I can't imagine a world in which we have to check people's genitals to make sure they're allowed in a fucking bathroom.

Anyways, I'd love to hear if this has given you a new perspective on things, or maybe not! Any questions are absolutely welcome, i'd love to answer any! I've put the two articles that I was referring to down here. If you'd like some more articles or studies about what I'm speaking on, I'd be happy to provide that! It's extremely important to keep making sure that you're speaking facts lol (and if you don't believe in science or smth, uhm... ig you only have my word for it then.) Anyways, I hope you have a lovely day and anyone else who is reading this! 

National Library of Medicine, July 2023. The Impact of Gender-Affirming Hormone Therapy on Physical Performance: https://pmc.ncbi.nlm.nih.gov/articles/PMC10795902/

British Journal of Sports Medicine, August 2026. Body composition and physical fitness in transgender versus cisgender individuals: https://bjsm.bmj.com/content/60/3/198

Note: if there's any inconsistencies or errors in my reply, I would love to hear any corrections!  

Please say trans women and trans men, instead of transwomen and transmen. I know you didnt mean anything by it, but transphobic people like to use that as a dogwhistle. Calling someone a transwoman is like separating them from women. Again no harm done but people will take that the wrong way so.