When I was in high school, twenty years ago, the Finnish participation in Barbarossa was painted in a very opportunistic, non-judgmental light. I remember my teacher stating that only six Jews were ever deported from Finland to Germany during the war. I haven't been able to find a source for it, but the point was to say that the army only took part to regain the losses from the Winter war and wasn't interested in Nazi ideology.
Only in recent years has there been more research and discussion of the nastier side of the Finnish front. I suppose much of it was known, it was just not appropriate to publicly talk about it. I have been wondering, just how much were things like the Einsatzgruppen a matter of public knowledge for other soldiers.
There is always more to be said but here is a thread from 2017 where several of our contributors including /u/Holokyn-kolokyn, /u/georgy_k_zhukov and I discuss Finland, its participation in German atrocties and related subjects.
While you wait for an answer from proper historians, I might dare to recommend some reading that you might find helpful.
Lars Westerlunds “The Finnish SS-Volunteers and Atrocities 1941-1943 - Against Jews, Civilians and Prisoners of War in Ukraine and the Caucasus Region 1941-1943” was published last year and contains the latest research on the Finns who fought as part of SS-Wiking division. It is very good and contains a lot of thorough research.
Andre Swanströms ”Hakaristin ritarit” is also good, tho lot less academic and some could argue that he goes a bit far in some cases when interpreting scant evidence.
As for the case with people fighting as part of regular Finnish forces, I have no idea and am curious too, so I hope you’ll get replies for this!