Once upon a time, there was a similar debate about black soldiers. The question then was, "shouldn't we put all of the black soldiers in their own barracks so that they can relax and not have to feel stress and pressure from white soldiers?" Eventually, rational thinking prevailed, and black and white soldiers realized they had a common purpose. While some bigotry and racism still exists, it has diminished to the point where black and white soldiers can now acknowledge their common humanity, live together in close quarters, and trust each other.
Perhaps someday, a question like the one posed in the original post won't be necessary. Perhaps someday, all athletes will recognize their common purpose. Is that day here? I wish I could answer with a strong "yes". But, we are close. Perhaps the question is best answered by the athletes themselves. The younger generation could care less about sexuality. It's only policy makers from older generations who seem to carry their prejudices of the past into the present day. It's only narrow-minded outsiders looking in without an understanding of the drive which brings these athletes to one place. It's only the ignorant who fail to understand the common bond formed between teammates.
The relevance of this question to the Deaf Community should be clear. You could just as easily have asked, Do Deaf people need separate housing because they use ASL and can't hear the doorbell? Are hearing people made uncomfortable because Deaf use a language Hearies don't understand? Are Deafies uncomfortable living in a world that fails to recognize them as capable human beings? Or, from the OP..."so that they can relax without fear of ridicule? Why do we need to?"
Seriously, do you need to ask this question here? Isolating a community because of a perception simply perpetuates misunderstanding. The more that the LGBT community is seen in the same light as the hetero world, the less fear and prejudice there will be. Can't we say the same about the Deaf Community? Maybe someday ASL will be taught in public schools right along side French and Spanish. Maybe someday a Deaf family will be able to go out to a restaurant and no one will stare when they sign through dinner. Maybe someday a police office won't assume someone is resisting arrest when all they are trying to do is communicate with their hands.
So, you want my answer... NO, you don't need to provide separate housing so that straight athletes can take a shower. NO, you don't need to provide separate housing so that LGBT athletes can sleep at night without fear of harassment. What you need is for people to get over it and grow up. What you need is for everybody to look at the person you fear and realize they are just like you. Black, White, Gay, Deaf... maybe someday is will just be... people.