The purpose of a protest is two-fold:
- To expand awareness of and public support for a particular problematic issue
- To challenge the legitimacy of established institutions and undercut the authenticity of those who condone, support, or enforce those institutions
Since the nature of these points implies that a significant portion of the populations is (at least initially) unaware of the problem at hand and tacitly in support of the status quo, it is difficult to make generalizations to the public at large. All we can really say is that the (again, initially) the number of protesters is roughly proportional to the size of the population impacted by the problematic institutions, mediated by the magnitude, intensity, and moral valence of the issue. Public solidarity will increase or decrease — perhaps increasing or decreasing the number of participants in the protests — to the extent that the protesters can present their point as a legitimate, morally sound complaint.
It's best to see this as a contest for legitimacy, played out on moral, intellectual, and emotional grounds. For instance, that recent Black Lives Matter — despite some problematic behavior on the fringes (like looting and destruction of property) — has largely succeeded in legitimizing its core issue while delegitimizing police and federal authorities. In part this is because the impacted population — black Americans — is large, leading to a proportionally larger number of initial protesters. But mostly these protests have gained traction because they have been able to make a convincing moral and emotional case that blacks are disproportionately targeted by police, and that has resonated with a far larger segment of the US population. By contrast the various contemporaneous anti-shutdown protests were initially smaller — even though the impacted population is significantly larger — and failed to gain the same kind of traction as the BLM protests because their moral argument is intrinsically weaker (in that no one is singled out for harm by the shutdown, and 'common good' counter-arguments are readily accessible), and they lack the same emotional appeal. A demand to be allowed to go out in public simply doesn't compare with a demand to be free of institutional oppression.
We cannot think of this process in simple numerical terms, though increasing supporters is part of it. It only takes one man with a strong heart and a sound moral conscience to stand up to a society, because it is that sound moral conscience that will sway the hearts and minds of others.