Deciding to wear your hair up or down during a massage is up to you. The massage therapist can work around your hair with whatever option you choose.
I find a lot of my clients with long hair wear it up while they are laying face down. After I turn them over, I request them to let it loose. With some techniques having it up can get in the way. Also prevents them from getting a good scalp massage at the end.
If you want to make sure none of the oil or gel get into your hair. Make sure you communicate with your massage therapist. Another option when lying face down is to put a towel over your hair – it cover’s your hair but still gives full access to your neck and shoulders.