Follow the logic of that argument and we'd never protest against anything that the self-appointed wise men of leftwing porotests gave holy permission for the masses to protest about. Oh, hang on, isn't that what already happens?
Seriously: the argument that we should never have mass protests against hardship in case the rigth co-opted it is patently absurd. It's effectively an argument for ensuring that protests remain small, elitest and ineffectual "for the greater good".
FWIW, the right is more likely to make merry hell with this issue UNLESS the left can get it's arse in order for once and launch protests over something that acually matters (in a big way) to vast numbers of people.