The October Revolution also inspired the building of Welfare States in the capitalist world.
Not really. The Depression and the War are far more responsible for that. You're not going to see much of a welfare state constructed in the 1920s in the aftermath of the Bolshevik seizure of power in Russia.
Yes, in fact red scare actually energized the right and helped to derail such programs. And the association with communism and support from such, was enough to taint a lot of proposals as well to the point that only the Depression finally created the impetus to advance them.
