Well, this is an interesting question.
Now, I don't think anyone would find out that you had this philia unless you told them, but I can't really say it would or would not hurt your credibility. As for me, I could care in the least. At least you have a job you *really* enjoy
All joking aside, I could see some people being uncomfortable with you cutting their hair if they knew. I don't really see why as long as you weren't groping them.
I will give some insight, I have paraphilic infantilism (mostly DL-side). It really doesn't take much to set off an erection, but I don't really have any sexual feeling unless I start them, or actually indulge(I suppose) into my desires. It's as simple as walking past the pharmacy at wal-mart, picking up a package of diapers, or a diaper at all; thinking about them, etc.~ to get an erection in most cases.
Even though it may be embarrassing, would anyone object to me being a pharmacist?
granted this is a slightly different situation when dealing with people. But, I hope maybe this helps a bit.
There are some arguments to whether or not any fetish, or any paraphilia is treatable. You could book an appointment with a sexual therapist (Got the right guy?), talk to your family doctor, other general practitioners, psychiatrists (in this situation?).
But in my opinion, unless it's really causing a burden or affecting your life, don't worry about it!