Should students be allowed to listen to their own music during class? In general, no, they should not. The brain can only consciously pay attention to one train of thought at a time, which means that if we're allowing them to listen to their music while they're doing seatwork, their brain is going back and forth, shifting its conscious attention between the music and what they're working on, which means their work will be of a lower quality because they're shifting their attention back and forth.
Now, I have heard teachers say that once they allowed students to listen to music just during silent seatwork, not when the teacher is talking, that that reduced the number of misbehaviors in the classroom. And that makes sense, but what I have never heard is that that increased the quality of the work that they produced, because again, they're shifting their attention back and forth.
Some students will claim that they need to listen to their music in order to stay focused on a particular assignment. And sometimes, that's true. There are students whose brains are kind of all over the place with their attention, and if they have one thing holding their unconscious attention like white noise like that music, then they are able to focus more.
But students who need music in order to focus on their work will have an IEP. It will a modification that all teachers have been informed of through the Special Ed department that those students need that. If they don't have that IEP, then that student does not need that modification. And usually, they're just asking for it because they don't want to deeply engage with the content because the content is challenging for them. So it's in our best interest, and in their best interest, not to let our students listen to music on earphones during any part of the class.