Perhaps the popularity of some songwriters with lesbians or gays in general is the gender neutrality of their lyrics--in contrast to the bulk of pop, rock, and c/w fare which is often quite sex-specific if not out-and-out sexist.
Many women (gay or not) may feel excluded by lyrics that make a lot of use of words like "man" as part of their rhyme scheme (like Lee Greenwood's "God Bless The USA"*) or that tie the love song to the physical characteristics of the (usually female) beloved.

Is it my imagination, or do female lyricists more often frame love songs in the second person (so you don't have to use personal pronouns like "him" and "her")? One song that comes to mind is Holly Near's song where she refers to the object of her affection as "sweet one," where a lot of writers would say "sweet girl" or "sweet lady" or "my lover man" or something else that's gender specified. A lot of Kate Wolf's lyrics (though not all of them) also could be sung from the standpoint of a gay or straight male or female. "Cornflower Blue" and "Give Yourself To Love" come to mind.

To the extent that singers/songwriters frame their songs this way, I would think they would be welcomed by people of various gender identities and preferences. That would explain why lesbians embrace the music of some women who have never presented themselves as "straight;" by not flaunting their heterosexuality in their lyrics, they, in effect, "embrace" the gay community in a way that much of "mainstream" music does not.

(But, then again, what do I know?)

Genie