Why would Illinois care if Y/N stole? They helped him get the artifact back and get to monkey heaven. Plus, isn’t he a Indiana Jones knock-off? Indiana Jones stole all the time.
Summary: He only didn't get upset or anything because he went with his gut instinct (and assumed) that we didn't steal it. Yes, we got it back to monkey heaven but again, if he knew how we got it, I think he wouldn't like that very much.
Well, I think he would be upset because at first he asks you if you had stolen this from a museum of some kind (he looks at you real suspicious at first) until he just goes with his gut and trusts you not being someone that stole that from said museum.
As we know, Illinois is mostly based off of Raiders of The Lost Ark (in which from my memory, could be wrong) is the more "morally" sound Indiana Jones so I think Illinois would go along with that too.