This is a fallacy. If there are widely trusted outlets for activism that in fact have little to no effect on policy, then we should speak out against them. This notion of "voting with your feet" and walking out does nothing.
So far as I can tell, the main purpose of the We The People site is to provide a scapegoat: a place for angry activists to vent their anger without causing real damage or wasting anyone's time with legitimate protests. In return, the president's staff must occasionally make a statement of the party line on some issue.
It's a neat trick funneling dissent into a neat little internet package. It defrays real activism ("Why are you taking action? It's much more polite to make an online petition.") and so it's worth decrying if you think it's really harmful. Merely refusing to sign is a tacit acceptance, and in fact is likely to just harm the issues you care about. Much better to sign, and then speak out against them if you think they are a fool's errand, as I am starting to believe.
Well, yes I agree with, just signing a petition will achieve nothing. Just like the man down the pub complaining about XYZ will achieve nothing except give him an outlet to vent. As the old saying goes: Actions speak louder than words!