They’ll beat and punish them regardless of the law. Haven’t you been paying attention?

I'm not a law-man, but my laypersons understanding of the law against impersonating a police officer hinges on intent. If you intend to deceive someone into thinking you're a LEO, and that can be proven (or can't be disproved beyond a reasonable doubt) it's illegal. Doesn't matter if you're in a suit trying to convince someone you're Special Agent Mulder, or if you're in body armor and a mask trying to convince someone you're ICE.

Also as an American I 100% agree with magikmw's point, that illegal or not it doesn't matter if ICE decides they don't like it - until you can manage to get in front of a judge, which may not be guaranteed. Then again even if you do, it has to be something you can reliably prove.

The absurdity of their lack of consistent uniform and identification aside, in this hypothetical the people start impersonating not simply because of their tacticool cosplay like ICE, but by being among them and accusing others of being the fakes, implicitly asserting they are the genuine ones. So if you happen to be tacticool cosplaying in the vicinity of ICE agents without taking action, then maybe you are in a defensible. But acting on that adds an element.

Of course, this would mean something except when dealing with a 'shoot first, ask questions never' scenario...

Remember that it's them who decides what's legal or not until maybe a judge/jury say otherwise.