One of the reasons why such rights as speech and petition for redress are supposedly protected is that retaliation in response to peaceful protest discourages that particular expression of discontent, and yet the discontent itself remains.
Discontent will generate some form of expression, whether you like it or not.
So if you will arrest angry people for blocking vehicular traffic and disturbing the peace, there is less incentive for them to march in the streets, and a greater incentive to do things less subject to identification and retaliation. For instance, someone might instead violate health codes when the state's agents are ordering food from their restaurant.
The more you close off and punish the relatively less harmful means of venting discontent, the more likely you are to see more harmful means, such as riots. And likewise, if those less harmful means are seen as relatively ineffective, people will do other things.
So putting protesters on a terrorist watchlist is, in a way, a form of self-fulfilling prophecy.