Some Protestant hymns like “How Great Thou Art” and “How can I keep from singing (a Shaker hymn)” are used during the Mass. Other than that, Protestant media is not used. I don’t think that it is out of doctrinal differences, but due to the structure of Catholic worship. The order of the Mass is highly structured and there are very specific rules. For example, people recently complained that Pope Francis celebrated Mass with flowers on the altar, which is forbidden.
I do not know the percentage of Catholics who listen to Christian music, but I am guessing that it is not that great. Again, this relates to the music we associate with worship. Speaking only for myself, I prefer the Latin hymns because they speak to the age and world-wide scope of the RCC.
Lastly, again speaking only for myself, Catholic worship is focused on the Eucharist. It has been said that the Mass is like a drama building to the point when the priest consecrates the host. So music and sermons (or homilies as we call them) play a secondary role IMO. In fact, there are Masses (usually early or weekday masses) where there is no music at all and homilies are kept to a few words.
That’s just my take. Interesting question, though.
I did not know that was specifically forbidden. Can you explain?