The difference is those groups promote culture for culture's sake. Capitalism does not. Culture is only promoted if there is profit to be made off promoting it. As such what culture exists is severely inorganic and dependent on market forces rather than being some proxy of the actual ideaspace of the community.
well, to be pedantic, stalinist tendencies of socialism (and leninist inspired movements as a whole), tend to prioritise culture as a way to communicate the ideals of the party.
Capitalism, in its most pure form, puts profit before anything else in any form of work
You've structured this statement in a way that makes it unfalsifiable: if culture is organic and thriving, it's because capitalism hasn't touched it; yet if capitalism has touched it, then it must be inorganic and inauthentic. You're doing a "No True Scotsman" on culture as a whole, defining real culture as something that excludes any evidence capitalism could've produced it.
There are plenty of counterexamples for culture within capitalist society (forgetting for a moment that it's bizarre to conclude that capitalist culture doesn't count as culture if market forces touch it): hobbyist communities, open-source software, Wikipedia, fan fiction, folk traditions, religious practice, academic subcultures, internet memes, the entire DIY/punk schtick, local theater, oral traditions. All of those are orthogonal to market forces.