Is the SPD even socialist?

When reading the lore and events of the SPD, I noticed that the SPD never refers to themselves as Marxist. In fact, the only faction that uses Marxist language (Hannover Group), gets a lot of pushback from the broader SPD. Even the Centre "Marxists" seem to view socialism as more of a means to an end of achieving a party state rather than an ideological commitment. As for the Neorevisionists, their ideology is grounded in urban left populism, rather than an authentic Marxism. This is compared to Liebknecht, who took an urban focus, but adapted it to Marxist theory. In fact, the SPD can purge the marxists in their camp after achieving the second mandate. With all that being said, can the SPD accurately be labeled as socialist? To me, it seems more in line with non-Marxist left nationalism, using vague attachments to Marxism as a lure for the German proletariat.