No you do not have to take your underwear or bra off during a massage. As always, you (the client) only undresses to your comfort level. If you want to take everything off that’s up to you – whatever you’re comfortable with.
It’s common for women to take off their bra off when getting a back massage to allow for a constant flow and preventing oil or lotion getting on their bra. Or you can leave your bra on and just undo the bra during the treatment. If you decide to leave your bra on, the therapist will work around it.
Some people will take their underwear off if their getting their glutes (buttocks) or their hip flexors worked on. If you leave them on, your massage therapist will work around them and use techniques without oil or lotion. You will be covered with the sheets at all times, except for the areas being worked on or in some cases the therapist will work over top of the sheets. Regardless at no point should your private areas ever be exposed or touched during the massage. If you don’t feel secure, make sure to convey that your therapist. You always have the right to stop or modify the treatment!