For example many CPSU members were formally members of the social democratic party, almost all Eastern Bloc communist parties were mergers of the preexisting communist parties with social democratic parties, and the Korean Social Democratic Party is one of the few opposition parties in the DPRK
Social democracy is not really the moderate wing of fascism. They have a history of collaboration with fascists, but they also have a history of fighting against them. It is best to think of social democrats are not being grounded enough in theory and historical experience to be consistent allies, and are vulnerable to being co-opted.
These days, calling social democracy the moderate wing of fascism is mostly a matter of insulting them (justifiably so). Especially since modern western social democrats have become full throated imperialists, and rarely even fight for workers rights anymore.
Sorry but your second paragraph seems at odds with your first. In my experience Social Democrats are pro-capitalism, which makes them no allies of Communists.
There’s a bit of a time and geography issue at play here. Modern Social democrats in the imperial core have become completely useless, and fascist adjacent in many cases, but Social democrats in the developing countries and during the early 20th century were much better. People who call themselves “left” or “social democrats” do not actually form a unified bloc with similar ideologies unfortunately, which makes calling all social democrats as moderate fascists even less applicable.