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No single standard can be used in all cases.  Obviously, if a person looks like a man or woman they are going to be admitted into a restroom regardless of what the person looks like without clothes.

In the case of sports, I think you are looking at technology that will be changing from year to year.  Science journals, sports governing councils and in some cases the courts must make the determination of a "probability of gender". 

Let's remember that we humans create situations where a determination of "man vs. woman" is necessary.  One hundred years ago we didn't have women only sports.  And if you define co-habitation in terms of a civil contract you eliminate the need to make a gender determination. 

As long as society paints itself into a corner where a determination must be made, then someone in society is always going to be unhappy with the answer.

As with many things in life, you must accept that chaos within boundaries is the only answer.