This really is such a fascinating subject!
There's been so many studies, papers and books on heterosexual women and their relationship with Mary but I do not think I have found something specifically focused on lesbians and how they feel. (Granted, my area of expertise concerns women from Latin America, so there may be studies done on non LATAM women I may not know about.)
That being said here some tidbits from the things I have been able to gather from studies done on heterosexual women, stories provided by lesbian women and how it all relates to their feelings towards Mary - also do note that the information provided below is specifically regarding the Marian apparition known as La Virgen De Guadalupe:
-It is important to note that whether lesbian or heterosexual, women that grew up with La Virgen De Guadalupe for the most part seem to follow her not with church doctrine as a basis but with folk religion instead. I am using this term to refer to practices of the faithful that incorporate cultural and regional practices into traditional Catholic doctrine. This also includes cases when such beliefs contradict church guidelines.
- To follow up on the point above the basis of the worshipping of Mary is not so much that she is the mother of God, but the sentiment that "Mary is a mother to all” alongside family stories of miracles granted, to quote the author Maria Del Cocorro Casteñada-Lilies:
"What gives veracity to the story in the eyes of the child is the context in which it is told to her or him. The story is not merely passed down as an event that happened many years ago but is contextualized in what the mother perceives as Our Lady of Guadalupe's intercession in the trials and tribulations of the family."
-In the same way some women thank La Virgen De Guadalupe for a safe abortion despite abortions being against church doctrine, so do lesbian women who thank La Virgen De Guadalupe for a homophobic parent accepting their orientation despite this also going against classical church teachings.
For examples of this there are some exvotos (an offering such as a painting or other artwork giving as a token of thanks for blessings) by lesbian women (and one by a bi woman) here: (x) (x) (x)
-Lesbian women who believe in La Virgen De Guadalupe also give thanks to her when surviving homophobic attacks, an example would be Cathy Arellano's story "Con una poca de gracia para la Juanita Doe", an English translation is available in Sinister Wisdom Issue 97 - Out Latina Lesbians. While I could not find a free copy of the issue online - here is pdf of the writing I am referring to (x).
-Outside of that, while I cannot provide too many details due to privacy reasons as these are personal anecdotes, two things I have heard from lesbian women that have stayed with me:
"When my mother kicked me out, I felt less alone knowing that there was another mother that would accept me no matter what - La Virgen De Guadalupe. I will always pray to her."
"I once made a joke about sticking with Catholicism because regardless of origin most other religions will always condemn the gays to hell so I might as well stay with the one I grew up with. Instead of laughing my mother became deadly serious and told me that was untrue. Orientation had nothing to do with whether or not I would be turned away from Heaven. Considering how Catholic my mother is, it surprised me but her next words did not: If I ever felt God was too distant for my worries, I could always implore La Virgen De Guadalupe. She is a woman like us and can understand certain things better."
For additional readings I would recommend:
Our Lady of Everyday Life - La Virgen De Guadalupe and the Catholic Imagination of Mexican Women in America by Maria Del Cocorro Casteñada-Lilies.
While her book only interviews heterosexual women, she does add that she wonders what she would discover if instead the women that volunteered were homosexual. Still a great introduction to how women navigate their faith through La Virgen De Guadalupe.
Chicana Lesbians - The Girls Our Mothers Warned us About - Edited by Carla Trujillo. Not based around religion but an insightful look into Chicana feminist writing. The original cover featured La Virgen De Guadalupe and I recommend looking into why it was removed for later printings!
And on that note... not specific to La Virgen De Guadalupe but to the general feeling of lesbian women and how they navigate their faith, I think this paper gives a good introduction -
Queer like La Virgen: Catholicism and Lesbian Sexuality in Carla
Trujillo’s What Night Brings by Emily Anderson (x)
(*I do also want to note that I have heavy disagreements with Chicana writing but nonetheless included two works with Chicana themes because I think it is useful for exploring how lesbian women navigate their faith. I also want to say that when reading Chicana writings to be wary of applying it to Mexican women as a whole as Chicana writing is specifically Mexican American).
Also as mentioned earlier my response focuses on lesbian women and how they navigate folk religion, currently I have yet to find writings on lesbian women that worship Mary (regardless of the Marian apparition), from a more strict theological perspective. There are a handful I have found that take this approach for devotions towards Jesus Christ but again not for Mary. (And the few that I have found have been from American or European lesbian women, which for both groups I am woefully ignorant of how they practice their Catholicism whether folk or strictly theological and thus wouldn’t feel qualified drawing conclusions for either group of women.)
Regardless of my own personal feelings on religion I really do wish a study would be conducted on lesbians that are devoted to Mary.
Hopefully this gave some insight to your question. I love learning about anything and everything, and tracking down lesbian experiences regardless of whether or not I agree with my fellow sisters really is a joy in itself!