There are actually several different laws involved here. The newest one is the NetzDG [1] (network enforcement act), that requires all reports of illegal content to be checked within 24 hours. The incentive structure is messed up because there are fines for failure to delete illegal content, but none for unjustified deletion. So the barrier was shifted from "obviously illegal" to "not obviously legal". The quotes in the Reuters article are all about that aspect of the law and of Twitter's enforcement.
The other laws that are involved here have been essentially unchanged for a long time and are not really controversial. They are just a bit more subtle than a random Twitter censor is going to appreciate, because they are intended for consideration by a judge. Under these laws, you can absolutely insult everyone equally, and Volksverhetzung is equally illegal, no matter which group it is directed against.
Edit: [1] The German text of the NetzDG is here: https://www.gesetze-im-internet.de/netzdg/BJNR335210017.html