The real-life SPD (and the KPD and DDP) supported repealing Paragraph 175 (and legalizing homosexuality), but they didn’t have the votes to succeed. The Prussian police under SPD control was also relatively tolerant and for the most part did not enforce the anti-gay laws. As far as I can tell, this did not become an electoral issue that negatively affected the SPD (which is not to say that the right didn’t attack them for it, just that it did not seem to move votes compared to everything else going on in Germany). Also, in the game, supporting LGBTQ rights does not directly increase popular support.