Should transgendered girls be allowed to compete in women's sports?
 
I can understand that there's an ideology that wants things to be equal, even genders, but we have to square that ideology with biology, or really, nature overall.

If we inform ourselves with biology, and not just ideology, then I would say that it is unfair for transgendered girls to compete in women's sports. The simple fact is that transgendered girls bodies still function as males, that is they have more testosterone, more muscle mass, more explosive strength than biological females, on average. That bodily make up would of course lead to better physical performance, especially when it comes to sports that require upper body strength. Based on this fact, I'd expect there to be evidence of transgender girls excelling in women's sports, on average. In a sense, there's already evidence of this if you compare the performances of biological males in sports with those of biological females.

You also asked why we don't hear about bans on transgendered boy competing in boys' sports, well one reason may be that transgendered boys won't have an advantage over boys, on average. If hormone replacement therapy has little to no effect on transgender boys, then I'd be worried that transgendered boys wouldn't excel much in such a sport.

One alternative proposal I've heard is create a sport just for the transgendered population.