Do women feel safer around gay men compared to being around straight men?
I will give a fairly mixed response.
Quite honestly, it depends on the men. Not their sexuality. The thing that makes me feel most comfortable around men is whether they respect people's consent in every day life. Things like asking permission before touching someone (this could be to get a leaf out of their hair, or guiding someone towards a door etc) unless there is an established consent between them. Things like not engaging in unsolicited communication with someone, or interrupting them when they're clearly wanting privacy.
I was with my partner in a park, eating some food recently. My partner, like me, is usually read as female. A man came up to us on a bike, ending a previous phone conversation as he approached with "hang on, I'm just talking to some girls". He then proceeded to ask for our numbers, ask if we wanted alcohol or drugs, and attempt to talk to us for quite a long time. We were pretty blatently not interested in him or wanting to talk to him. But he didn't leave us alone. That was uncomfortable. Had either of us been alone, it could definitely have been pretty scary.
I've been harrassed multiple times on the street, when alone as well. Yes, I'm quite sure these were all straight men. And if a woman were to do something like that, it would be annoying, yes, but it would be unlikely to have the same feelings of fear and power dynamics about it, because when men harrass it is usually about (probably unknowingly) asserting their dominance and power over someone they consider to be a woman, much more so than expressing attraction or asking them out.
I'm not saying I feel less comfortable around straight men than gay ones. There are plenty of straight men who don't treat me or other people poorly. There are plenty of gay men who a) treat the people they are attracted to poorly, and b) can therefore be expected to treat other people poorly as well. Gay men aren't immune to patriarchy and cultures of harrassment and entitlement over women's bodies. Gay men and straight men alike, of course, are not beholden to it and are fully capable of being a person I would want to be around. And many are.
If someone comes up to me and says "don't worry, I'm gay" I won't feel any safer for it. What will make me safer is genuinely something along the lines of, "Hey, sorry to interrupt. Can I [insert whatever thing they wanted from me." If it's someone I know already, then I should hope I choose to associate with people I feel safe around.
Lastly, I'll add something that I haven't experienced, but people I know have, which is gay men excusing their behaviour (which usually involves breast groping) by saying "it's okay, I'm gay". No, it's not okay, and that's sexual assault whether or not you're attracted to the person you just assaulted.
TL;DR Respect the people you interact with, and they'll feel safe around you. Your sexuality doesn't matter.