Most of my friends had long hair. Mine was down to my butt by age 17. And most of our fathers had the same haircut they wore in the service, mine included. It created some tension but I don't recall any major blowups over it, for any of us. They understood the difference between true rebellion and the trappings.
I can only draw on my own experience. My parents were very Old World European, with a strong emphasis on honesty, obligation, respect and achievement. As long as we met those criteria, they didn't sweat the small stuff too much. But they also kept a close eye on us so the small stuff didn't become the big stuff.
It was all out war at my house with my sister vs. the rents. She was absolutely livid when they wouldn't let her go to Woodstock with her boyfriend (she was 14 at the time). Him going out at midnight to get her from parties, then listening to the incoherent rambling from her room till sunrise (she could hear colours, apparently). 2 years later, married with a kid. I think rebellion was her middle name.