Is it forbidden to remember God and seek His help during a sin, such as asking for facilitation of permissible exercise while forbidden music is present?

Whoever mentions the name of Allah Almighty, seeking His help in committing a sin, has committed something unlawful. He does not commit disbelief unless he considers it permissible or performs it in a manner of disdain. Practicing sports in a place where there is music is not inherently forbidden, but one must denounce the wrong by requesting the music to be turned off. If you are unable to do so, then look for another hall, or use lawful stratagems such as wearing headphones to listen to the Quran.