I can speak from experience on this to a degree I think. I grew up on rap music, hip-hop, whatever you want to call it. When I was younger, I used to have conscience attacks, and toss all my rap cassettes in the trash. My mother would sometimes go through my music and pitch what she found immoral. Later as CDs replaced cassettes, I would build a collection, and either I, or my mother would toss those too, only to relapse occasionally. Nowadays I still listen to some of it, but some of the language makes me cringe as I've gotten older. I can't tolerate explicite sex talk any longer. But some of the 90ish-early 2000ish angst still appeals to me for some reason. Loved CMW's Music to Driveby, and Ice Cube's Death Certificate.
But going back to Christian music...... I don't know if you're familiar with a chain of fast food joints called Chik Fil A? They play gospel music in their independent stores. Now typically I would get their tenders and potato wedges in the mall where you would just hear mall music. However when they built their own little spot in a local shopping district, I stopped in. I ate there, while reading a newspaper. The gospel music made me uncomfortable. Really uncomfortable. To the point I almost took my food to eat it in the car. I toughed it out, but I havent been in that joint since. Its ridiculous looking back on it. Thinking about it now as I'm typing, I think I justify my listening to questionable music the same way most people justify watching violent movies whether they're JW or not. The same way Schindler's List was on national television at 8pm when children were still up and people justified it based on it being historical. However gospel music has a different effect on my conscience. My whole life I've had the Babylon the Great teaching shoved down my throat. From my childhood onward I've been taught to view Churches as the dwelling and lurking place of demons. I view the Cross around people's necks with pitiful disgust. Catholic Priests are synonymous with pedophiles to me, one in the same even though one of the most wanted in the US is a former JW Elder. You get the point though. "False Religion" is looked upon more harshly than questionable entertainment amongst JWs. I can see why that woman was uncomfortable.