Anyway, it wouldn't really be "their" tax dollars paying for the music you like, any more than it would be your tax dollars paying for their Christian music (remember, there's no discrimination in what's purchased). Faced with also having their free Christian music taken away, I'm pretty sure they'll ease up in their opposition. It's better to think of it as your tax dollars paying for the music you like, their tax dollars paying for the stuff they like.
I hope that if ever a law like this were to be passed, you would continue to be concerned. But, I gotta say I always find it annoying when people criticize what might otherwise be a wonderful idea, by arguing that some people might be stupid about it, so we shouldn't do it. It's time to stop being so afraid of stupid people.
Government pays for and administers roads, the military, the justice system, and a host of other things that are much more abusable than our entertainment. They don't completely mess up all those other things, and I don't think it's likely to go badly when it comes to music. Given that the worst thing the government could do would be to not pay for certain things, meaning the artists would have to sell the music just like before, that's not exactly devastating.