From what we know... Are our characters actual criminals?

Since the story in this game is limited and I'm still quite inexperienced when it comes to 40k overall lore...

This question came out of all a sudden to me when I replayed the intro mission, seeing Zola somewhat hesitant to immediately brand us as heretics or as criminals at first sight, like she did with Wolfer.

Then I paid attention to the possible options we can choose as bio background during character creation, and most of them seem like we were just at wrong place, at the wrong time, whether it was actions or words someone didn't like.

It's not like our characters actually pledged loyalty to a Chaos god, killed someone innocent or something like that, is it?

Or am I missing something here?

I just want my big man to be an actual good man and not some crazed psycho who's justifiably part of a penal legion...