I grew up in the 90's and my parents were strict, particularly compared to a lot of my peers. Things like watching television was heavily restricted. I remember making similar arguments to my parent's deaf ears "I won't fit in, all the kids at school will be talking about what they watched on TV last night, I'll be a loser" etc.
My experience was that most of the kids didn't care that I couldn't understand their Simpson's references or whatever. If anything they were sympathetic, I would get a lot of "man your parents really suck" and then kids would shrug and move on.
I did resent my parents growing up. Looking back I think they were pretty clear examples of "tiger parent" stereotype. I felt immense pressure and stress to achieve good grades and it honestly felt like nothing I did was enough to make my parents happy. I get along with my parents now as an adult but as a teen my home life felt very unhappy at times. I can remember the relief I felt when I left home to live on my own.
So I think it is more likely your child will resent you, then them being ostracized by their peers.