If a large number of people attend, you will not know what is happening some distance away. You risk being caught in a crowd you would not wish to be associated with. Watching any confrontation between demonstrators and police, it is usually clear who the agitators are from a dispassionate distance. The police, however, do not have that luxury and can overreact in the heat of the moment, under a hail of bottles and bricks.
If you are genuinely concerned about your professional standing, better to find another way to protest.