Must men only sponsor men, and likewise with women?
Is it suggested anywhere in AA literature that men only sponsor men and women only sponsor women?
This isn't a rule but simply an evolved custom.
From the AA World Service pamphlet "Questions and Answers on Sponsorship":
Can any member be a sponsor?
There is no superior class or caste of sponsors in A.A. Any member can help the newcomer learn to cope with life without resorting to alcohol in any form.
In most instances, A.A. custom does suggest one limitation, already noted previously: If the group is large enough to allow a choice, sponsor and newcomer should be of the same sex. The reasons are the same from both viewpoints; we A.A. members, no matter how long we have been sober, remain thoroughly human, subject to emotions that might divert us from "our primary purpose."
With gay AAs opposite gender sponsors are common and often encouraged.