Personally, I think the music industry benefits by the trading of MP3s as more people are exposed to the music, many of which will eventually purchase the CD and/or attend the concerts of the recording act in question. I also think newspapers and magazines gain a wider readership by exposure on sites like Free Republic. (Though it would help if we all got in the habit of clicking the source link so that the web traffic of the sites providing the articles are duly compensated.)
There are a number of issues here. While we conservatives may not agree with the RIAA's members on many (most/all) political stances, what's at stake here is simply protection of private property. In short, the musician or artist who creates the song lets the record company distribute it for him or her. And don't give me this nonsense about how it's unfair: the record companies take all the risk. They have the right to control distribution of intellectual property, just as book publishers have the right to control distribution of their books. If you went and photocopied a book, you'd clearly be stealing. This is basically the same thing.
As far as FR posting articles, sure it's done, but we don't post articles from places that really object. Most of the other sites that we post from probably don't mind (if they did, they'd tell us, and we could only post excerpts from then on). The sites probably don't care because it drives some traffic to their site, and with sites, traffic is what matters. I'm sure that posting articles from small town newspapers increases traffic to those sites as some people click through, whereas if there was no post here, no one would click through. If we posted articles from a site that charged for access, I'm sure most people would agree that would not be a good thing.
As far as increasing exposure to the music, that's the record company's decision, not yours. You aren't in charge of marketing Avril Lavigne's music, and EMI, or whomever she signed a contract with, has that responsibility. They may decide to release some of her music as "freeware". And then you can copy it. But if they don't, you can't. That's way beyond any fair use. It's sort of convenient that by copying all this music for free, you're really benefiting the record companies, isn't it?