All perfect praise be to Allah, the Lord of the worlds. I testify that there is none worthy of worship except Allah and that Muhammad, sallallahu ‘alayhi wa sallam, is His slave and Messenger.
It is legitimate for the person who hears music to plug his ears, following the example of the Prophet, sallallahu ‘alayhi wa sallam. It was narrated by Naafiʻ, the freed servant of ʻAbdullah ibn ʻUmar, may Allah be pleased with them both, that "Ibn 'Umar heard the sound of a shepherd's flute, so he put his fingers in his ears and diverted his mount from the road. (As they rode on) he would say, 'O Naafiʻ, do you still hear it?' I would say, 'Yes.' He would then continue riding, until I said, 'No (I no longer hear it),' so he let his hands down and returned his mount to the road. He then said, 'I saw the Messenger of Allah, sallallahu ‘alayhi wa sallam, do like this when he heard the flute of a shepherd.'" [Ahmad and Ibn Hibbaan. This is the wording of Imaam Ahmad]
It is not a religious innovation to plug the ears, and it is not a religious innovation to carry something with which you can plug your ears when you hear music either, because there is no difference between plugging the ears with the fingers or with anything else. Rather, plugging the ears with something is easier than putting one's fingers into the ears for a long period of time. Doing this would not be considered a religious innovation just because the Prophet, sallallahu ‘alayhi wa sallam, did not carry something with him to plug his ears with. Music was not quite widespread then as it is in our present time.
Allah knows best.