Did you ask what happens to your deposit if you adhere to their cancellation policy? Is it refunded to you, or are you charged a deposit no matter what?
Imx, it's customary for many salons to hold an appointment with a credit card number. This is to cover them in case you're a no-show. I've never complained, as it seems only fair - give proper notice of cancellation, or prepare to be charged for the appointment slot. Particularly since my appointments last about 3 hours... why should they block off all that time from other potential clients and then be left holding the bag if I flake off? My current stylist, who runs her own show, doesn't do this. But I wouldn't blink if she did.
However, I've never been charged a deposit in advance. If this is indeed what they requested, in place of a credit card number, then I would be a bit taken aback.