Should the recitation of the Qur'an be stopped at a university graduation ceremony that includes musical instruments and intermixing, or is reciting it better than leaving it even under these circumstances?

If the ceremony includes forbidden acts, then the first duty is to denounce them. If denunciation does not help, then it is not permissible to participate in it or attend it, due to His (Allah's) saying: "And He has already revealed to you in the Book that when you hear the verses of Allah being denied and ridiculed, do not sit with them until they enter into another conversation. Indeed, if you did, you would then be like them."

Opening occasions with a recitation of the Qur'an has no basis in Islamic law. Some scholars have deemed this act an innovation (bid'ah). The prohibition is further emphasized if the celebration contains forbidden acts, because opening such forbidden acts with a recitation of the Qur'an shows disregard for it. Therefore, you must ask the administration not to open such celebrations with the Qur'an, and you should not attend or participate in them.