I am married and looking for a non-sexual relationship with a
female--a soul mate kind of thing.  I was thinking that the safest
approach for this would be to hook up with a woman that is gay, but
doesn't find men offensive.

The most simple way would be not to think of her as a gay person. My
husband is straight (he'd better be ;-) and one of our best friends is
gay. This is not why we're her friends and this is not why she's ours:
if you look for friendship in general, you'll meet all kinds of
people.

Maybe, an idea for *real* friendship is to engage in a voluntary
activity, where many women are involved: women's shelters, helplines,
feminist organisations.

If you are married, do you mean to imply that your wife isn't your soulmate??

I don't think there is anything wrong with having friends outside of
marriage, but I'm concerned by your questions as for looking for a
soulmate. It seems as if something quite large is missing from your
marriage itself to be looking for such a deep connection from someone
else other than who you're married to. Have you though of why this may
be?