How to explain to college that religious observance precludes me from living on campus, as required?
This kind of letter should typically be brief and straightforward. Unless they have told you specifically what should be in the letter, you can write:

To whom it may concern:
Please be advised that, as a Muslim, my religious observance precludes me from living on a coeducational campus. As per the advice of [person or office who told you to write the letter], I am writing this letter to request an exemption from the on-campus living policy.
Thanks for your consideration,
Nimbra

If you want, you can also include contact information for a member of the clergy (i.e., a religious leader) who knows you and can vouch that you do, in fact, have such a requirement. (Sometimes this is required as a matter of policy; for example, those who cannot take the SAT on Saturday due to religious observance must provide a letter from clergy attesting to this.)