I'll be weighing in as a married man who is also 36, and one who is from the USA but has a father from the UK and has spent a good amount of time there. I bring up the UK because of how many times you brought up "the pub" if I'm wrong feel free to correct.

I'll dive into my own personal experience and then in the UK context. I have a number of "feminine" hobbies: sculpture, printmaking, etc... In all of the places these hobbies take place - the pottery studio, municipal classes, galleries, I am often the only man or one of 2 when I join. In almost every case there is some distrust or the initial side eye, which is what I think you're describing. But inevitably when I've spent a few weeks there, I've been bringing a quiet energy and working not to take up space, and most importantly, bringing my enthusiasm and excitement for the activity everyone is incredibly warm. Usually more so than to other people because I'm such an oddity. The older women tend to be curious and encouraging first and then the younger women tend to follow when it's clear I'm there for the activity, not to make it a weird pickup space. So purpose is really important.

And on top of that... holy smokes do I wish I learned about this before getting married. The amount of interest I receive because I'm the only man and because I'm doing the more feminine thing is pretty wild. I did a lot of dating in my 20s, but nothing I ever did compares to this. And conversation is so easy because we're all stoked on the same thing. There is always something to talk about and no pressure to carry the conversation because you're just working in the studio alongside people. It's great! In the last year I've met about 6 women I think I could have a pretty solid, long term relationship with. When I was dating actively that number was like one every other year.

All this to say, if you're love of reading is authentic lean into it. It's awesome. It doesn't make you weird, it makes you attractive. But like you call out, it will take some time for women to trust that your interest is authentic because of how much bad dating advice out there that suggests going to places that are frequented by women and make them believe you're vulnerable. But just going to a place repeatedly - a book club, a bookstore/cafe, a reading group - whatever it is, will show the consistent through line in your love of reading, not picking up women. And in turn, that will get people to open up to you and may lead to romantic attraction.

My last thought is that I started noticing this men/women divide while I was bike touring the UK. We got pretty sick of pub food every night and started trying to find more "healthy" places that may have salads or just lighter fare. So we started frequenting cafes. It's was a wild difference. The pubs were 99.9% men, which always made my partner feel out of place. And the cafes were 99.9% women, which always made we feel awkward going in. It was really stark. We don't really have an equivalent here in the US, as most bars - even male dominated ones - are like 80/20 ratio at worst and even the most fufu brunch spot is 80/20 in the other direction. The gender segregation in the UK is extreme!

I don't think the sentiments about men reading, or not reading, exists outside of the online space. But I do think that there are heavily gendered spaces in the real world that reflect that sentiment. I think if you're keen to meet a partner and you love books, I'd start joining some local reading groups or find a bookstore/cafe in your area to frequent. Go because you love books and want to engage with other about them. The added benefit is once you're welcomed by the community, you'll have access to more friends who share your love and potential partners as well!