From a ethical standpoint, is it fair to let transgenders compete in all-women competitions?

It would interest you to know that the International Olympic Committee studied this issue for several years. After that study they announced in early 2004 that under certain guidelines trans people could compete in their identified gender. Several other athletic associations have since adopted the Olympic guidelines. Since the announcement in 2004 there has been 8 Olympic Games and not a single medal has been won by a trans person, not one. In fact, there hasn't been a single trans athlete that has even qualified to compete in the Games. On a wider scale, trans people have been medically transitioning for more than 70 years. In all that time I can count the number of times a trans person won any kind of professional championship on one hand.

So the main take away from this is:

With transition and the guidelines in place, trans people don't have any advantage over other athletes. Therefore it is ethical to let trans people to compete. In fact, I would say it's unethical to not allow them to compete given the history described above.

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Trans women, yes. Trans men, no. Not all trans people are MTF

There's not one set of transgendered people. but males and females have different changes going through puberty,. which alters your body for the rest of your life.

but honestly I think we should de-segregate sports. we did that with the navy and now it's just whoever meets the requirements, period.

There should be rules.  Time since beginning of transition, actual hormone level testing, especially prior to major events, and doctor certification.  A genuine 'man' would be unable mentally tolerant MTF hormone regimen for a year.

I think it should depend on how far a person is along their transition. If we are going to continue dividing people on gender or sex lines, then a trans woman or a trans man should compete with cis women and cis men respectively bc in the course of hormone replacement therapy, their secondary sex characteristics (notably their musculature and fat distribution) reflect the gender with which they identify rather than the one assigned to them at birth.

That is to say, trans women who have been through a sufficient length of time of hormones and had transitioning procedures (based on my understanding) do not have a biological edge on cis women. They may be taller/have longer limbs, but I would think compared with the general population women in sports (depending on the sport) are often taller than average. And height depending on the sport can be a disadvantage.  

You could make the same case for trans men. It would be unfair for trans men taking hormones to compete against cis women.