Protesters are frequently classified as terrorists. Protesters frequently escalate their tactics when non-violent methods fail.
It takes a lot of willpower to keep to the moral high road when you can see the folks walking on it ahead of you getting their asses kicked.
The rights to free speech and petition for redress in the U.S. are not universally respected by those targeted by the criticism.
In that context, placing a protester on a watchlist has all the appearance of malicious retaliation for exercise of a protected right.
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.
In other words, I'm full of shit unless someone backs it up.