Do I give my cat away?

We aren't home very often, only really at night and during breaks and days my mom has off work, I've had my cat since 2020, she's a very sweet girl but I'm usually not doing mentally well so I find it exhausting to care for her, I love her and obviously do care for her even if I find it exhausting, now my mom knows I've thought about giving her to another family member before and told me her friends are looking to adopt another cat, they already have one cat and one dog, my cat gets along with other animals fairly fine, however the friends are a gay male couple, my cat does not like biological men at all, she freaks out at even my grandpa who she has seen more than once, now I know she doesn't have any trauma revolving around males because there was a single woman taking care of her from the time she was born till she was old enough to be adopted, and then we took her in and there are no biological males living with us, I think it's just because she grew up around biological women, I have no doubt she'd eventually warm up to these two men and they could give her a lot more attention since one of them doesn't work.

My question to you all is should I let them have her? My judgement right now is clouded because I've struggling really badly rn and my emotions are all messed up, I don't want to be selfish, so I'm asking for all of your opinions, I have met them and they seem like a very nice couple and again already have two animals so it isn't there first time caring for one, they can also care for her better and give her more attention than I can.