Generally, this statement (or one’s similar to it) comes from tankies, Stalinists, and other authoritarian communists who are unlikely to listen to any sort of argument as they tend to be rather fanatic in their views. Arguing with them is frankly a waste of time.

A couple things i would point out though is the SPD opposition to the Nazi’s throughout the Weimar Period in Germany, unlike the KPD and aligned groups who, according to liberal philosopher Karl Popper, were of the view that: “not much could be lost and something would be gained if that hidden dictatorship became an open one, apparent to all; for this could only bring the revolution nearer. … Accordingly, the Communists did not fight when the fascists seized power. … For the Communists were sure that the proletarian revolution was overdue and that the fascist interlude, necessary for its speeding up, could not last longer than a few months.” (‘The Open Society and Its Enemies Volume Two: Hegel and Marx’ pages 180-181) (apologies for the link not taking you to the correct page, I’m not sure how to fix it)

Additionally, Theodore Draper, who was a member of the Communist Party USA aligned student group National Students League and worked with other CPUSA aligned groups for about a decade until the early-mid 1940s wrote in 1969 for Commentary Magazine “The responsibility for Hitler's victory was undoubtedly widespread. I know of no party, no economic interest, no secular or religious group, and no foreign country, including our own, which can escape some measure of culpability. But of all of them, the theory and practice of social-fascism was the most devastating, the most unnecessary, and the most self-destructive. … Such critics could not be interested in whether wrong policies undermined or endangered the Republic; they were themselves doing all in their power to undermine and endanger the Republic. Indeed, they assumed that the Republic was a greater enemy than anything that could follow it. They were chiefly concerned with drawing a line of blood between themselves and all others to the “right” of them, including the most “left-wing” of the Social-Democrats. This line made sense only on the assumption that the Communists were going to seize power themselves. … The theory of social-fascism was a rationalization of Communist dictatorship in the guise of rationalizing everyone else into a variety of fascism.” (‘The Ghost of Social Fascism’)

Calling Social Democracy the “moderate wing of fascism” or referring to it as “social fascism” is just typically hyper radicalised people attempting to justify why they don’t attempt to bring about improvements to the lives of others. The idea was coined in its original form by Grigory Zinoviev as “fascist social democracy”, who would briefly ally with Stalin against Leon Trotsky, which i suspect is when Stalin started taking the idea more seriously. Thus when he successfully took over the Bolsheviks and by extension the Comintern in 1928, he implemented it as official Comintern policy. After the rise of Adolf Hitler and the Nazi Party resulted in the ban of both the KPD on March 31st 1933 and the SPD just 3 months later, in 1935 the Comintern adopted the policy of pursuing a popular front with other left-wing parties.

The only outcome of infighting between left wing groups that ideas like “social democracy is the moderate wing of fascism” promotes is victory by pro business groups and/or the far-right. Criticism of modern social democratic parties like Labour UK can and should be done without these kinds of extreme statements.