Dinner with Rabbi Rachel
I’ve switched the pens I’m using and a couple of other things, and I’m still getting used to that. God forbid I should be consistent.
Anyway, I must confess I did no research for this. Maybe a rabbi would say, sure, it’s no problem to marry two gay gentiles. I suppose it would depend on the type of rabbi. Anyway, that would have gotten in the way of my joke. I’m sure this answer is at least plausible.

Nope, you’re right about one of them needing to be a Jew. Unless she’s a conservative rabbi, then both of them would need to be Jewish.
Oddly enough, I wasn’t even thinking about that angle, even though it’s my punch line. I was thinking that, as a member of the clergy, your primary obligation is to your congregation. You might think a person would say, sure, you’re an old friend of mine, and you just need someone who can legally sign and file the documents, I will marry you. But in reality, you, as a rabbi or minister or priest, represent your church/temple/synagogue, and you can’t just do whatever you, personally, want. (It’s hard to convey all that in five lines of text in a comic.)
In our own case, in our original wedding, our minister was Unitarian. Unitarians will marry people who are not members of the congregation, but even so, there was a process we had to follow. There were meetings to discuss relationships and what makes a successful marriage, so that she could feel confident, in solemnizing our union, that the relationship was real and strong.
Not just Conservative Rabbis – only half of Reform rabbis will marry an interfaith (at least one Jew) couple. So, I know a lesbian couple in which one partner converted so their Reform rabbi would officiate.