If your uncomfortable use a bottle, I'm sorry but a man is no different to a woman. Before DH I dressed to attract male attention because that's normal. Breast feeding under a cover is no different to having lunch at a beach club in a bikini. Infact I think my nursing bras were bigger than I would ever buy a bikini!
I'm not pro breast feeding other than the first few days for antibodies after that expressing and sharing the load is a lot more beneficial to women+baby. Allowing them the freedom to escape if needed or return to work. It's even the simple things like hey DH pop in and change DS + give the bottle, whilst I run into this shop. If you say men can't go into baby rooms so you can get your boob out that isn't needed for breast feeding, your saying more woman who make the smart choice to share the load equally are dragged back a decade to being the main care givers. It's also about the baby bonding with dad and teaching another generation of boys that a baby is 100% 50:50.
Luckily these are baby rooms to protect the shared paternity of the BABY! I went back to work when DS was 3 months and DH stayed home, he was never as welcome at baby groups etc as I was. This needs to change it needs to be that men and woman are 100% equal. To say that breastfeeding is more important than closing the gender pay gap is quite frankly insane. Even the small benefits of breast feeding don't out weight any risk of pushing back shared care even by the smallest margin.
Also if we move to 100% shared spaces it should help woman feel less threatened by men (who can be threatened by a species that has a very sensitive organ hanging out of its body) and help with the perception that looking at a woman in a sexual way or paying her a complement is in some way an insult or a threat.
As a strong independent woman I never ever consider gender its simply Steve, or sarah etc. Me and DH are also a pair we go together and help each other achieve and enjoy life, I do not think he should be told where he can and can't go just because someone else is scared. I also think men should have to accept woman using currently male spaces, tho they might hate that as it makes the line even longer.
The sooner everywhere is simply the WC, baby room, changing room etc the better.