It's been mentioned that a bug prevents you from removing crewmen between missions. The game will put them back when the next mission starts, unless they're dead (or arrested--see below).

Evidently, the "crew bug" is in all the digital versions including Gog's.

I played the Police campaign but not the Mafia campaign. In the Police campaign, there are a couple of clumsy workarounds, in which you can get rid of lower-rated officers to make space for better ones.

You do this by getting them killed or arrested!

A character gets arrested after the mission if he builds up enough FBI Warnings. These happen when he carries out a false arrest, or beats up or murders civilians. I think another cause is when he shoots a mobster who isn't considered a threat.

I'm not sure how many Warnings are necessary. And possibly it will affect this less if you've unlocked the Court, but I don't know.

A blue padlock will appear on the cop's profile.

A murder instantly creates enough to get him arrested.

Being arrested isn't permanent like getting killed. E.g. without realizing it, early on one of my guys racked up a lot of Warnings and wound up in jail for most of the game. When he was finally released, he returned to the inactive roster without bumping out the guys I'd been using.