What is the ruling on exercising in a hall that plays music, knowing that advice to the management was not accepted, and is it permissible to wear MP3 headphones during exercise to avoid the music?

It is impermissible to listen to music, and its presence in the training hall is a reprehensible act that must be denounced. If denouncing it verbally is not possible, then denouncing it by heart requires leaving the reprehensible act and exiting its place, as the Prophet, peace and blessings be upon him, said: "Whoever among you sees an evil, let him change it with his hand; if he is not able, then with his tongue; if he is not able, then with his heart—and that is the weakest of faith." This is also indicated by the Almighty's saying: "And He has already revealed to you in the Book that when you hear the verses of Allah being denied and ridiculed, then do not sit with them until they engage in another conversation. Indeed, you would then be like them." You must denounce it verbally and offer advice, and if they do not respond, then look for another hall.