Socialism is completely incompatible with free markets. Free markets typically stop being opinionated beyond the concept of enforcing contracts/consent, i.e. people are allowed to structure their economic relationships with one another however they want, they just have to respect their agreements.
Socialism is a prescriptive ideology, it is concerned precisely with the nature of the economic relationships people make. Labor theory of value. "From each according to their abilities, to each according to their needs." Workers own the means of production. To the degree that people are able to freely structure their economic relationships with one another, then the vast majority of those relationships will look nothing like the prescriptions of socialism. To the degree that the economic relationships are made to look like the prescriptions of socialism, then the economic model would fail to be described as a free market.
This is why in a free market/"capitalist" economy, communes can exist, Mondragon can exist...because you can structure your relationships with one another however you want. It's just that most people don't like that structure. "Capitalism" itself doesn't care at all if that's the way people want to distribute equity and control of the corporation. Now, if you want to structure an arbitrary economic relationship in a socialist communist country...good luck.
Not sure why this comment is downvoted. In the context of Marxian Socialism and Command Economies, it's very much true that socialism is incompatible with free markets.
Going even further, without a free market for labour, there's no true worker emancipation. Even with "worker-ownership" (read corporate-ownership under a democratic governance), each worker's power is still diluted by the governing body (which, funnily enough, means socialism strengthens capitalism as "control by those who own capital" while weakening capitalism as "free markets").
>> Capitalism is ... OTOH socialism ...
> No, socialism is not ... and capitalism is ...
I often wonder if these classifications have long outlived their usefulness, and only lead to endless, often heated, ideological discussions about their definition. To the extent that those benefiting most from observably-broken-form-of-global-capitalism can use that as a tool to sow division and strife and ensure nothing changes. The gist of your and parent's comment is the interesting bit, where new systems and mechanisms are discussed.