I'm not sure if it was the same way in the 60's and 70's, but every protest I saw in Chicago since 2003 always attracted a fair share of professional protestors. Your "Free Tibet"ers, environmentalists, and various others always seemed to show up for Iraq War protests and immigration protests. It's easy to ignore protesters when they are obviously doing it as lifestyle choice rather than out of honest indignation.
There's not much you can do about such people showing up, though, unless you have a very organized, centrally run protest with a gatekeeper for who's allowed to show up. People who have their pet issues will show up and attempt to use the platform if participation is open. I guess you'd just need enough new people to swamp the 'regulars'.
(These kinds of things are, incidentally, why Lenin-style communists argue for agitation to be tightly organized by a vanguard party, which keeps things on message and makes sure protests and other actions maximize tactical and strategic effectiveness, rather than becoming an incoherent free-for-all. But Leninist organization isn't too in favor on the contemporary left.)
