From a follow-up chain in this spectacular answer from /u/commiespaceinvader on "How dirty was the Wehrmacht":

I'm curious, the 20% that [found ways not to participate in mass atrocities, according to Browning's excellent Ordinary Men, which shows how everyday people were slowly corrupted into becoming racist genocide participants], what was their fate? I mean, was there any reasonable way to avoid doing war crimes?

In the overwhelming majority of all cases: Nothing. If I am recounting correctly, there are only two cases of people refusing to participate in mass murder facing serious consequences such as a court martial.

All in all, not participating was done mostly by claiming to not have the stomach for it. Usually, superiors would excuse you for that but of course you'd have to face the social pressure from your comrades.

As there are miniscule number of cases of people being persecuted, there are also a miniscule number of cases of people outright refusing. Mostly it was done by saying one is not up to it or by reporting sick or by requesting a transfer to a different unit.