The original NSDAP was quite socialist, and even as Hitler developed it into his own party, it retained a strong socialist faction, which we now refer to as the Strasserites. It was purged eventually, but the history is there.
FWIW, "red-brown" political alliances are still a prominent thing in some countries, usually based on shared social conservative ideals. Furthermore, there are political movements such as National Bolshevism that explicitly draw this connection.
