If it blocks traffic, legally it needs a permit. (Or is this just some/my municipality?)

No, that would be an incredibly narrow reading of the bill of rights. It's also not how Americans have ever interpreted their rights. Blocking commerce has a long history as a form of protest in the US. It was used in the revolutionary war, the great railroad strike, the pullman strike, the suffrage movement, civil rights, etc. A lot of ink has been spilled trying to draw lines around what "peaceable" means and when a blockage becomes unpeaceable, but it's universally acknowledged that the bar is somewhat higher than whatever local ordinances happen to decide on.

Let's talk some more about the civil rights example though. MLK was famously arrested for his part in the Birmingham campaign for demonstrating without a permit. His response was to write his "Letter from a Birmingham Jail" [0], where the famous quote that "Conversely, one has a moral responsibility to disobey unjust laws" originates. He directly addresses this issue of permits later in the letter:

    For instance, I have been arrested on a charge of parading without a permit. Now, there is nothing wrong in having an ordinance which requires a permit for a parade. But such an ordinance becomes unjust when it is used to maintain segregation and to deny citizens the First-Amendment privilege of peaceful assembly and protest.

[0] https://www.africa.upenn.edu/Articles_Gen/Letter_Birmingham....