I disagree about the "anti-democratic" nature of those things. They're a way of increasing the visibility of a point of view. People are often fearful of change, and of standing out from the crowd. Making it obvious that there's a crowd to join gives such people greater confidence to express their real opinions.

Is that all sad and rather pathetic? Absolutely! Nonetheless, it's human nature and we have to work with it.

It's also an opportunity to get publicity for the arguments, so that more people may be convinced, which may be a little more to your taste.

You're probably right that petitions and protest marches tend to have little immediate effect (although there are exceptions, such as England's poll-tax riots, as opposed to the peaceful protests in Scotland that changed nothing). But longer term, they can build awareness and possibly help (indirectly, obviously) to change opinion.