Is one who exercises in a gym where music is played, in deference to the wishes of some members, considered sinful, knowing that he does not pay attention to it and that the majority of gyms do so?

It is not permissible to subscribe to clubs where forbidden acts are practiced, such as music, and one should search for clubs free of such things. If a Muslim is a member of a club where reprehensible acts occur, he must condemn them to the best of his ability, or seek another club free from Sharia (definition) prohibitions. Furthermore, not paying attention to music does not permit sitting in places where it is played without necessity, due to the implicit approval of the reprehensible act.