How disruptive are they? The media says so but you never know with them whats really goin on.

I was there for a month.
Saw a few very small and sad demonstrations.
Nothing that would affect tourists.
There were some attempts to block parts of the ring road.
Police are getting much more aggressive about keeping roads open, especially when the protest blocks access to a hospital. The most common protest was the same three sad jerks on Dam square with a drum and a megaphone.
When not protesting, they can be found crying on the floor of the self-help section of your local bookstore.

Weasel