Generally speaking, on the Eastern Front, it was common on both sides not to take prisoners as a matter of principle in many units. Part of this was simply the reality of life there-there were times where you just had to shoot or leave to starve your own men who were wounded beyond help-but this was a war of annihilation between two sides that hated each other with a primeval, casual zeal that would have been unheard of on the Western Front. (Here's an example from the diary of a German soldier called Wilhelm Peter Reese: one day, his unit discovered the mutilated bodies of a bunch of German soldiers, some of which came from their unit. As a result, they decided that they simply weren't going to take any prisoners for the rest of the month. What struck me was the tone of the order-it was as if they were simply deciding what to have for dinner in another life, and that's when it hit me that this sort of thing happened literally every day on the Eastern Front.) And this wasn't the worst that could happen to you: many soldiers-one example being the frequent isolated German pockets of resistance at Stalingrad after the surrender of Paulus-fought to the death because they figured a quick bullet in battle was a better end than starving or being worked to death in the other side's respective concentration camp system. The Russians were absolutely terrified by the fall of 1941 of being captured by the Nazis and simply being left in an open field to cannibalize each other.

With that being said, SS men were particularly likely to be shot without question or worse by Red Army units, as the atrocities of the SS were well known and they encapsulated the Nazi ideology that had wreaked such woe on the Soviet Union. There was also something of an ideological impetus: I'm pretty sure that German soldiers would have been more likely to execute GRU or NKVD men out of hand as well, even without orders from the top. And Hitler's Commissar Order, which stated that all GRU/NKVD political officers were to be shot immediately, probably meant that they simply saw this as a logical response.