Equality under the law is the solution.

The reason criminals dress up as cops, be they local cops or single issue fedcops (e.g. ICE) is because they wanna kick in a door and it's the only profession where a small team kicking in a door is considered normal by the populace so it's the one they want to dress up as. If you just wanna be somewhere it's easier to pretend to be a plumber or whatever.

If you make that door kicking of a criminal-ish sort just as illegitimate when the cops do it as when anyone else does it the problem evaporates. Cops, especially in small numbers and out of uniform, shouldn't be kicking in doors as part of "business as usual". That's the kind of thing that they know they're gonna do in advance, so they should bother to show up in several squad cars, have a warrant, and heck, have a lawyer on a Teams/Zoom call ready to explain the warrant.

If anybody could put a bullet in anybody who forces entry without producing a warrant without fear of state reprisal (i.e. if normal self defense rules for whatever state you're in apply) there'd be almost no value in pretending to be a cop for the overwhelming majority of crimes people pretend to be cops for (home invasions, mostly).

But the FBI will never advocate for that solution because at the end of the day they too are more equal animals.

The bad guys wear masks.