Is it permissible to wear earphones to listen to the Quran while music is playing in sewing workshops, or is that considered a lack of proper respect for the word of Allah?

There is no objection to listening to a Quran recording via headphones in a place where there is music, as what is forbidden is the intention to listen to music. As for hearing it without intention, there is no sin in it. And since music has become prevalent in workplaces, it is not forbidden to remain in the workplace. You should offer advice and condemnation to the best of your ability, and you have fulfilled your duty, according to the Almighty's saying: "Allah does not burden a soul beyond its capacity," and His saying: "So fear Allah as much as you are able."