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I literally spam him at 4am about yaoi, my boyfriend says he's happy to see it. I usually have a hard time expressing my feelings, but not with yaoi. So, he says he's glad that I do it. This probably didn't help your issue, but if you ever need someone to talk about bl or just anything you're struggling with, (anyone reading this actually) I have discord! Just respond to my message and I'll dm you it. Have a great day/night.
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I wouldn't outright tell my partner that I read yaoi. I'd just ease them I to it like "dude look at this scene in a manga I'm reading it's fucking hilarious", that's actually what I do with my best friend. I don't tell her that I read yaoi but I'll sometimes send her a screenshot of a character and say "look at this man, his tits are bigger than mine". There was this jojo doujin that was recommended to me, there was a panel where Jotaro had arms longer than my lifespan, I thought that it was hilarious so I sent my friend a screenshot of the panel.
Just ease them into it, show them funny parts of the manga you're reading or show a character that was obviously made to be sexually appealing and make a joke about it, so that when they see that you're reading bl they won't think twice about it. In the end, just remember the golden rule: don't confuse fiction with reality.
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I've only ever told my brother and my ex friend. If I were to date someone, idk, I feel like I would still value my privacy a lot, and I don't see the point in telling him/her that I like yaoi because I don't see anything wrong with it but I also don't see the need or why I should bring it up. But if i were to tell them and if they were to be judgemental abt it because they don't know it at first I would just explain what it is and say it is a hobby that I enjoy, if they continue to be unsupportive I would consider breaking up. Theres no point in dating if You're not compatible.
This kind of scares me because it's literally my favourite thing to do and it's also my way of coping now but i feel like there is a lot of judgment attached to reading manga and BL at that would be like cherry on the top. I would want to be open with my partner but I'm also scared of the judgment.