The two ideas are not mutually exclusive. They are, as Jonah Goldberg pointed out in his Liberal Fascism: The Secret History of the American Left, From Mussolini to the Politics of Change, commonly associated.
They are commonly associated because socialism requires a "New Man" in order to succeed. For the Russian Communists, it was the "New Soviet Man." For the Nazis it was their "master race" of Übermenschen, but either way, it requires those "others" to cease to exist so that they'll stop gumming up the works of their scientifically- and socially-engineered utopia.
Yes, the socialists were all in favor of "the workers," as long as they were the right type:
Source: The Soviet Story
It is suggested that Shaw was using satire here, to poke holes in (as Wikipedia puts it) "the eugenicists' wilder dreams," but the fact of the matter is, joking or not, his call for chemists to "discover a lethal gas" for carrying out mass killings was eventually taken seriously. And it wasn't satire that killed millions of Ukrainian kulaks, it was deliberate starvation, starvation that the New York Times' Walter Duranty covered up, saying "Must all of them and their families be physically abolished? Of course not - they must be 'liquidated' or melted in the hot fire of exile and labor into the proletarian mass." Nor was that the first - or the last - mass murder carried out in the name of socialist utopianism.
Mass murder isn't a bug with socialism, it's a feature.