The closest direct source I found suggests that there is a negative correlation between system-justifying beliefs and collective anti-system action. If people believe voting legitimately is a means by which they can enact social change, they are less likely to organize against the system itself. This does not mean voting itself is against organizing, in fact organizers vote at higher rates than non-organizers. The importance here is that collective action is diminished when that is directed towards engaging with the system itself.