In order to tackle the issue of transgender sports participation you need to first decide why women sports exist.
If the purpose of women's sports (i.e., the reason men aren't included) is to provide a setting in which women can associate and form friendships/bonds then I think it is appropriate for trans-women to be included. In other words, if it is like a sorority trans-women should generally be included. On the other hand, if women's sports exclude men primarily because men are physically dominant and they don't want to compete with them, then I don't believe trans-women should be included. There is NO DOUBT (none, zero, zilch, nada!) that trans-women have significant physical advantages.
It seems to me that in professional sports men are excluded because of their physical competitive advantages. For that reason, I don't believe Trans-women should be allowed to compete professionally. The more complex issue is for high school athletics, which is more about personal improvement and socializing than it is competition. I think I would allow trans to compete in high school, but track separate individual records for them (i.e., goals scored, swim/run times, etc.). I would not allow trans-women to compete against natural women in college, because I think it is more about competition.