The difference for me boils down to if you can be seperated from the action, or if the action doesn't cause another to stumble.
Like Jeremyr said, a Deacon owning a liquor store... that would definately cause some folks to stumble.
In the instance of playing music, you have to get more involved in the process than merely pushing buttons, or stocking a shelf, cutting grass, or other such occupations. As a Software Engineer, at a company that is not Christian I can code all day, and when I leave the desk, I take nothing with me. (And before someone says it, "Yes, I have turned down many projects because the product could be a stumbling block for others, and No I don't watch television shows, or read literature that is not beneficial for more. Remember God is not a respector of persons, so if You wouldn't feel comfortable following a man of God who does said action, you should probably refrain from it as well.)
Playing music is a SPIRITUAL act, whether you guys want to acknowledge it or not.
So that the post is not only based on my opinion lets put some scripture to it.
Can a believer play secular music? The answer in short is "YES" But we have to ask ourselves is it beneficial to our Christian walk? 1 Corinthians 10:23 "All things are legitimate [permissible--and we are free to do anything we please], but not all things are helpful (expedient, profitable, and wholesome). All things are legitimate, but not all things are constructive [to character] and edifying [to spiritual life]." - Amplified