Pretty much anyone in an adeptus or of high enough status has immunity from local planetary laws and customs (even this isn't perfect defense with the shoot first ask questions later and the innocence proves nothing mindsets of the setting) but no one is above the laws of the Imperium. However it would be a political and bureaucratic nightmare to go after particular people. It can even be tricky for Inquisitors to take down some people without suffering political backlash of some sort.
Also immunity wouldn't mean anything to a fanatical cleric with a flamer who thinks you are a heretic so why would it mean anything to a fanatical arbitrator with a shotgun who thinks you are a criminal. The 40k universe does not come across to me as a place where yelling "you can't do this I have legal immunity" would do any good when facing down an official of any major organization that is armed, fanatical and thinks you are guilty of something.
An armoured man covered in gore steps out of the burning cathedral. When the [fanatical cleric with a flamer who thinks you are a heretic] and his soldiers accost him, he simply claims diplomatic immunity in the name of the feared Inquisition and waits for a few days in custody until he is freed by a mysterious benefactor.
A terrifyingly augmented Magos cuts down every worker of plant 421-75-9, accusing them of Tech-Heresy. do you really think a single Arbitrator will dare threaten or kill such an obviously important personage?
No. They'll just get him to a trial and get rid of the problem by passing up their chain of command - a process that will let their "victim" leverage his own immunity and get his own side involved. Voila!
Remember that the horribly convoluted Imperium will always help - and that anyone with Immunity has enough resources to avoid the "summary execution" side of things for the few hours necessary to leverage his immunity.