I work quite closely with a massage therapist (in general, they don't really like being called 'masseurs' and 'masseuses' any more because these terms can carry sexual connotations). He works out of one of the gyms that I also work at, so this is an exercise context, as opposed to a spa.
He is a man and there is a sizeable proportion of female clients who don't want a male massage therapist.
A woman client asking for a female therapist, or not wanting a male one, is completely, utterly normal and no one bats an eye about it. (And nor should they — but a surprising number of clients can be a bit shy about asking, because they think it's unreasonable to ask. It isn't.)
My colleague is wise and experienced enough to know that being massaged is a highly personal experience, that for some women it comes with an element of perceived personal risk, and that him being a man is enough for some women to feel uncomfortable.
At our gym/studio, the receptionist will ask the client at the booking stage if they have a preference for a male or female therapist. It's never left to be sorted on the day; in other words, no client would be put in the situation of getting into the massage room to discover that her therapist is a man when he walks into the room.
Good massage therapists will see the person on the table as a collection of connected musculature rather than a person, if that makes sense. The way he talks about it, he sees clients' bodies as a kind of engineering puzzle or (sometimes) an issue to be worked around, or a problem to be solved (if there are back pain issues or similar).