If you don't specifically mean 'inapproriate' as yaoi, then yes I'm (pretty) sure they suspect.
I mean, my parents caught me reading porn manga when I was on 6th grade (tho in fact I've been reading since earlier than that), but it's just nude girls and stuffs (no sex).
Then, my mother knew when I posted Akise & Yuuki kissing scene picture on FB.
......
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