Firstly, while there is certainly no shortage of shockingly uninformed individuals in most any modern society, it's also the case that in general, members of those modern societies have an historically unprecedented level of access to information. Most take advantage of that to at least some degree. For "big issues of the day," like the situation in Gaza (to use the most currently relevant example), the large majority of people are aware of the situation. They probably lack a good portion of the facts of the matter, but they're aware of it. A protest isn't likely to impart any of those missing facts, nor is it really all that likely (imo) to stimulate a previously-unaware person to seek out those facts: if someone is so disinterested in the world around them as to not be aware that something important is going on in Gaza, then I very much doubt they'd be the sort of person to dive into fact finding because someone blocked a bridge.
It's a similar situation with my second point: is a disruptive protest really likely to motivate a person who's not previously been inclined to take action to do so? I'd be very surprised indeed if the percentage of those who do so exceeds low single figure territory, save perhaps at the very beginning of the situation, before it becomes widespread knowledge. And if anything, the percentage of people sufficiently infuriated by a disruptive protest who take action in opposition to the desired outcome of the protestors might actually be higher. Our rather shitty species has always been more likely to act on annoyance than altruism.
Protests in general preach to two groups: the choir, and to a disinterested congregation who won't respond in any meaningful way to the protest. The choir doesn't need motivation; the congregation (for the most part) can't be motivated. It's probably the case that protestors' efforts could be better spent in aiding their cause in other, more direct ways than in trying to reach the tiny percentage of people who are not yet convinced and are inclined to actually do something to advance the cause. I think this is particularly true of disruptive protests, when that small number of motivated fence sitters have to offset the number of people turned into opponents of the cause.