As someone who has somewhat researched this topic, largely for the sake of some of my friends, I can say with confidence that transgender people should be allowed.
After one year (the amount recommended by world athletics) of HRT (hormone replacement therapy), the only conceivable advantage a transgender woman (Male to female) has is a 9% faster mean run speed, on average, and this only applies if we insist on total fairness, which I would contest is not conformed to in current sports, such as many top athletes being very tall, which I would argue makes just as much of a difference, if not more than AGAB (assigned gender at birth).
It is interesting to note that in the same study, transgender men performed on average better than their cisgender counterparts, due to HRT.
I'd also tend to agree with @AmericanPie, and their point of where else they would play.
And finally, not to get too political, whether or not you agree with their being allowed at the Olympics, I'm sure no one could argue that new tory laws prohibiting transgender students from PE class (you heard that right), are anything but simply ludicrous.