There's no indication that Aveline goes after any apostates (who are not serial killers or something). It's not her job. Homicide cops can arrest drug dealers just for drug dealing, but they usually don't.
Aveline doesn't go after apostates... but she also covers up their presence from legal authorities whose lawful duty it is to go after them. In your analogy, Aveline is the homicide cop who sits ontop of a drug den because she has friends involved who benefit her, even as she happily shuts down other other criminal actions that aren't her job.
Is it her job? No- and neither is accompanying Hawke. Is it special favors and exceptions in violation with the spirit of her role and duties? Absolutely. It's not Aveline's job to hunt apostates, but it's not her job to help harbor them either.
So I'm hearing that either time Hawke is always a criminal for one way or another.... But Bethany gets taken to the circle, so thusly Warrior/Rogue Hawke isn't criminal there - becuase they didn't make her a GW or something, so yeah, their not criminals if Bethany is taken to the Circle...
Rather, Hawke stops being a criminal (because he/she can no longer conduct that crime) for that particular activity. They might be a criminal if, say, conspiracy is an extended crime- the entire point of the Deep Road expedition is to corruptly buy safety for an apostate- but the crime of harboring an apostate ends.
Not that there aren't many, many other activities of questionable legality for Hawke to partake in. Breaking, entering, and manslaughter on the basis of hear-say- ie, the typical quest in Kirkwall- can provide plenty of opportunities for even an unimaginative prosecutor.
What would that make Blue/Dimplomatic Hawke?
A smooth criminal.
-insert gif-
More seriously- it makes a point of author awareness failure because the writers clearly didn't put much consideration into Hawke being anything but another RPG character outside the law. Mass Effect had spectre status (with a bit of being a terrorist) or 'lawless' space, KOTOR had the Jedi/Sith privilege, Jade Empire had you opposed by the Evil Empire in the first place. Even DAO had the Warden exemption- not only are Wardens uniquely above the law in the name of the Blight crisis, but Loghain was the enemy- anything you did not only had Warden/Blight privileges, but also the fact that the laws you were breaking were of an illegitimate authority.
Thing is... DA2 lacks that. Kirkwall isn't an illegitimate authority. It's corrupt and troubled, but it's far from the Evil Empire, and Hawke lacks any special legal authority or exemption. Hawke gets away with things because Hawke's strong enough to kill those who resist, and bribe enough of the rest, even as Hawke rises to power based on those two things: money, often questionably gained, and killing people who disagree with Hawke's desires.
No one bothers to ask if Hawke has any right or justification to kick down doors, kill guards, and loot the homes of total strangers just because someone else asked them to. Stealing every piece of junk that's not nailed down, selling pants that someone presumably stored with the intent to sue... it's never even questioned. It's just ignored in most cases, and handwaved in others- hey, it's self defense, they attacked us- even if Hawke's basis for being there is weak in the first place.
It's just never thought through, and rarely justified. When you recruit Fenris, you go on a rampage and basically take over Danarius's manor. You find it empty and infested with demons, which is convenient... but it's not why you're there, is it? You went there to kill a guy. And if the manor had been populated, you would have killed them too- maybe not the servants (maybe- if they didn't attack first), but you would have wiped out all the guards like you do everywhere else because why not. And even when Danarius isn't there, Fenris just... keep it. Squat in it, waiting for revenge, basically stealing private property (loathsome as the man who owns it may be), and it's all good because Fenris is with us and the Captian of the Guard looks the other way. And no one even questions if she should.
Hawke isn't some victim of an illegitimate authority- there is a legitimate authority, imperfect as it may be, and Hawke ignores it because we're the PC and we do what we want. We grow in power. We even threaten to take the mantle of legitimate authority ourselves. And we never question if we ourselves are legitimate because of course we are. We're us, and our companions must be good too because they like us and help us, and so we don't question them because they amuse us and we're all that matters.
It's this really, really bizaar lack of introspection that leads people to go 'Varric is the best person of the cast', practically the moral paragon of reasonableness and morality, when our introductory scene to Varric Tethrass is of an idle-rich aristocrat casually shooting a poor thief for the sake of a good impression and a lucrative business deal.
And we're supposed to root him on, even as he slugs an already pinned, pained, and submitting would-be theif... because, by god that little rat stole from us! That was our money... which takes, like, an hour to earn thirty times more.
/ Sarcasm on
Of course, he also a criminal. All Hawkes are criminals, and criminals all his friends too.
No, Hakwe's friends are criminals if and when they break crimes. No guilt by association here- it's complicity in crimes, or some other action. Aveline is corrupt because she personally enforces uneven application of the laws and standards on people based on personal whims, frequently for her personal interests and benefit. Varric is a blackmailer because that's what he does, when he does go around having fun adventures and telling tales of shooting people poorer than him. Isabella's a slave trader because, by canon, she's engaged in the slave trade.