At least one Muslim has flown in space
Back in 1985, Saudi astronaut Sultan Salman flew as a payload specialist on Shuttle flight 51G. That was in the days when a representative of the company owning a satellite being launched on the Shuttle could fly as a payload specialist. Flight 51G launched the Arabsat A satellite.
There's no reason why Moslems couldn't fly to the moon or Mars, but they should go as a contributing member of the crew rather than some form of affirmative action. By that, I mean they should be someone with a skill necessary for the mission, such as flight surgeon.