Clearly I haven't read the books. People from the Capitol seem to be doing a pretty well living, they even have luxury and stuff. Why would they want to protest against the regime? Or is it only districts 2 to 12 fighting against the dictatorial regimen on the third movie?
By and large the population of the Capitol don't protest against Snow's regime. They've very indoctrinated that the Hunger Games are a vital part of their history and often turn a blind eye to the poverty in some of the outlying districts (it's widely agreed that the situation gets worse as the district numbers increase).
An example of this is at one of the feasts where they provide a drink which makes the consumer sick so they can eat more... a concept Katniss (from District 12) finds astonishing.
However there are sympathisers, people who are willing to go out on a limb for the districts. I don't want to go into too much detail if you've not read the books on who these are but as evidenced by their actions in both Catching Fire and Mockingjay there are indeed people in the Capitol who feel the system has to change.