Of course the justices aren't a jury, and their rulings concerning constitutional law don't resemble jury decisions. I would be glad to have a lesbian on the court, for reasons similar to the ones you've cited. But this way of thinking about the court also has its dangers, since it probably involves uncritical notions of "subject position."
Incidentally, the latest news suggests that Kagan may not be a lesbian; but whatever the case, there's apparently a whisper campaign against her -- not for the first time in recent court history. A question that strikes me as more interesting, maybe, concerns the religious backgrounds of the justices, a matter that embroils us a little less in assumptions about subject position, identity, or experience.
@ Mr. Stone:
I see that you touched on most of the topics I was going to address while I was typing my post...
"But this way of thinking about the court also has its dangers, since it
probably involves uncritical notions of "subject position."
See: Clarence Thomas.