The pin says "Legalize Poly".
But, overall, being polyamorous is perfectly legal. (Except with regard to marriage.)
What's happening regards polyamory is that it's culturally and socially taboo in most places. Are there places where it is outright illegal? It's not illegal in the USA. But it can get you in trouble with family, friends, co-workers, employers -- and the military if you are in "the service" (where it is in some sense "illegal").
As I understand it, most practitioners of polyamory are deep in
the closet -- which puts them / us in a very similar situation as gays back prior to
Stonewall. But there is a
major difference which gives polyamorous folk a tremendous advantage in coming out, as contrasted with pre-Stonewall gays. For pre-Stonewall gays, the practice of their orientation was
illegal as well as taboo. You could be ostracised, shunned and humiliated -- or beaten (or worse), albeit illegally -- for being gay in those days, but you'd not be handcuffed by the cops and taken to jail. You were not at risk for jail or prison time.
It is
way past time for all of us poly folk to step out of our closets. Visibility is strength.