I think it was fair in the past, but in the age of Justin Beiber I think men's haircuts must take quite a bit of time. there should be prices determined by length of hair and discussed at the beginning before the hair cut. I have thick long curly hair which needs layers etc. dh has short hair which takes ten minuts to cut, it would be fair for us.
It's a hangover from the days when men all had a short back and sides, which was easier. I remember the awful culture shock I got eight years ago when I moved (with baby DS) from my inner-city flat to my parents' suburban house, and needed a haircut. I had been used to getting my then-very-short hair done at the local barber, but the suburban barbers nearly shat themselves when I walked in and flatly refused to do my hair.... (no wonder I first shaved it off and then grew it to the point where all I have to do is ponytail it and it doesn't need thinking about...)
Dh took our DD's to his barbers for a no frills basic haircut but they wouldn't do them. His hair is very thick and at times pretty long so I would think he would present more of a challenge and time drain than them.
I think, broadly speaking, hairdressers have had more training in dyeing, styling and layering long hair etc.
I see it as barbers providing a basic service (for example - queuing system rather than appointments, not bringing you a cup of tea and a magazine, not washing your hair first and putting product on it afterwards, not having more complex services like colouring available) and hairdressers as a more in-depth service. It takes an hour for me to get a wash, cut and blow dry - DH gets done in a lot less than that.
OP, I'd think you'd have more luck claiming the barber is discriminating against you by not letting you go there even though the haircut you want is one that they offer, than by claiming its a tax.
I know it's not the primary point, but if you want to save money on haircuts there are lots of excellent tutorials on YouTube teaching you how to do it. I only go to a hairdresser now for a restyle, trimming long hair is too easy for me to pay someone else to do it.