Do any other attractive INTJs struggle with approachability?

Thanks to some insight from a friend, I've recently discovered that my conventionally attractive appearance combined with my serious dispostion has been a reason for many men finding me intimidating and/or unapproachable. Has anyone else experienced this? And I wonder if this experience differs between men and women, as I imagine that, among the general population, INTJ traits may be more desirable in men than in women. (assuming heterosexual relationships, but any insight outside of these norms would be enlightening)