socialists do not support capitalism, meaning they want workers to control the means of production
Workers controlling the means of production sounds like co-operative industries. This paradigm is not antithetical to 'capitalism' in the sense that there is still private ownership of the means of production. I disagree with the statement that democratic socialists do not support capitalism.
A good debate on this topic here - https://politics.stackexchange.com/questions/323/are-worker-cooperatives-socialist-capitalist-or-their-own-category