The word protesters has for obvious reasons jumped into abnormally high-rotation on the news radio dial, and to my surprise, many of the members of the media (on NPR and the BBC) that I've heard use the word are pronouncing it protésters [pʰɹəˈtʰɛstɚz] rather than the way I would pronounce it, prótesters [ˈpʰɹoʊˌtʰɛstɚz]. (Please ignore the r-coloring I've indicated on the last vowel, which reflects my r-ful pronunciation; it's the difference in stress that I'm interested in.) I think I've pinpointed both the justification for pronouncing what I'll arbitrarily call "the media's way" and why I pronounce it my way; read on below the fold if you're interested, and let us know what you think in the comments.
protést [pʰɹəˈtʰɛst] is a verb meaning "to express an objection to what someone has said or done". There's also a noun derived from this verb, prótest [ˈpʰɹoʊˌtʰɛst], "a statement or action expressing disapproval of or objection to something". (Definitions from the New Oxford American Dictionary.) It's quite common for related noun/verb pairs like this to differ in the placement of stress (witness récord/recórd pérmit/permít, etc.), and the secondary stress on the second syllable of the noun is (arguably) a reflex of the primary stress on that syllable in the verb from which the noun is derived. So far, so good.
The agentive -er suffix attaches to verbs to create nouns that (roughly) have the meaning "one who verbs": a runner is "one who runs", a worker is "one who works", etc. These derived nouns tend to keep the verb's stress where it's found in isolation: "one who perfórms" is a perfórmer and "one who rállies" is a rállier.
If you're following along so far, you will have noted by now that this all points to the media's way of pronouncing protéster as correct: add -er to the verb protést, and that's what you get. But not so fast.
You see for me, protést is primarily the action of an individual with a specific grievance, while prótest primarily describes a group event and many grievances. In other words, I wouldn't describe the act of someone who protésts to my analysis here as a prótest, and I would also be very surprised to walk by a prótest and to hear them chanting "We protést!" So protésters doesn't work for me because the folks we're talking about aren't protésting; they're involved in a prótest.
So does this mean that -er can (irregularly, exceptionally) attach to nouns like prótest? I don't think so, because it turns out there's also a verb prótest — in my vocabulary at least, and likely derived from the noun — that means roughly "to be involved in a prótest". Add -er to this twice-derived verb, and you get my way of pronouncing prótester.
So now what's up with the media's way of pronouncing it protéster? A very reasonable and likely explanation is that for these speakers, the verb protést is simply not confined to describing the actions of individuals with specific grievances, but also covers the actions of groups with many grievances. This explanation would appear to entail that these speakers rarely if ever use a verb prótest with the more specific group-action meaning; this remains to be seen.