The e-mail could go something like this:
"You're one of my favorite artists and I love your work! Now I won't be supporting you because of the position your performance rights organization has taken. I hope you can continue to create wonderful music without my financial support, not that I'll be enjoying them."
I'm all for copyright reform, and I abhor the positions of groups like ASCAP and the RIAA, but I don't think boycotting the artists is the right step to take.
For example, let's you love a great independent band but you're upset they've signed with an RIAA-backed major label, and you won't purchase their new album because of your disdain for the RIAA, and other people do the same. So, the new album is a flop. The major label realizes and decides that this small act wasn't ready for the Big Time, and drops them off the label. Now your favorite band has a failed album, they've lost their outlet with which to release their work, and if anything they're in debt from the entire experience. The RIAA is no worse off.
ASCAP is different because they do performance rights, not the releasing of music, but the effect is the same. Boycotting artists that you like just because they are affiliated with ASCAP won't hurt ASCAP, there will just be fewer artists that you like who are able to be successful.
How about an e-mail to your favorite artist that says "I love your work and I'm happy to support you, but I'm concerned about the positions that ASCAP and the RIAA are taking. Have your considered releasing your work through alternative channels of distribution?"
A thousand musicians who can't make a living through the "system" and get dropped aren't going to change anything, but a thousand musicians inside the "system" who can lobby these groups to modernize absolutely could.