[acsrp38]

You are half right
Congress shall make no law
Nothing in the Constitution prevents state and local governments from regulation assembly
Read the 10th amendment.

It's the hipocracy of the LOCAL government that decides
that certain groups can protest and not others

[oh8eleven]

"The powers not delegated to the United States by the Constitution, nor prohibited by it to the States, are reserved to the States respectively, or to the people."

I'm no lawyer or scholar but my understanding is that since the Constitution declares the right to peaceful assembly, no state can write a law restricting that right.
Perhaps I'm just too naive .... and freedom loving.