According to their site they have permits, and they are doing local organizing in every state.

I’ve not personally verified it, but they claim to be doing this legally.

this what you call an “illegal protest”

No, I think this could have been organized a lot better, but as far as I know it is legal. According to the ACLU:

• Your rights are strongest in what are known as “traditional public forums,” such as streets, sidewalks, and parks. You also likely have the right to speak out on other public property, like plazas in front of government buildings, as long as you are not blocking access to the government building or interfering with other purposes the property was designed for.

…

• You don’t need a permit to march in the streets or on sidewalks, as long as marchers don’t obstruct car or pedestrian traffic. If you don’t have a permit, police officers can ask you to move to the side of a street or sidewalk to let others pass or for safety reasons.

• Certain types of events may require permits. These include a march or parade that requires blocking traffic or street closure; a large rally requiring the use of sound amplifying devices; or a rally over a certain size at most parks or plazas.

• While certain permit procedures require submitting an application well in advance of the planned event, police can’t use those procedures to prevent a protest in response to breaking news events.

https://www.aclu.org/know-your-rights/protesters-rights

However I’m not a lawyer, so if you know for a fact that these demonstrations are illegal I’m eager to learn more about it.