Capitalism is a game where only a few people get to win.
We have also seen time and time again that it is a game that is able to manipulate and change whatever ideology or behaviour you have to work towards its own benefit.
So the only way to actually "win" is to not play the game.
Right now that seems impossible because it is a massive collective action problem, however this whole platform is a testament to show that it's possible to overcome that kind of problem.
Reddit is a dominant platform that is starting to destroy itself. People are in turn finding alternatives such as Lemmy to satisfy the need that Reddit once did.
I view capitalism in the same way. It will never truly completely cease to exist (the same way Digg never truly died), but it can become irrelevant over time if we collectively decide to just use another system to satisfy the same needs that capitalism is satisfying today.
The one example that I can think of that tries to tackle this problem is the idea of free stores that are based on a gift economy. If more people decided to use this system instead of capitalism then capitalism will have less sway over people's lives.
And in the end it doesn't have to be specifically a free store that needs to be adopted by wider society but whatever it is does need to satisfy the same basic need that capitalism does in our current society.
"Capitalism" just means that the industry (or specifically, "means of production") can be privately owned.
The whole idea of Lemmy is allowing smaller groups / individuals to own smaller instances, so we don't depend on big corporations.
So the way I understand it, it's more of a big vs small thing, not really a "private" vs "governmental/social" ownership thing.
Sure, Lemmy gives freedom for people so, even governments, can make their own public instances.. but this all still relies on capitalism, since individual instances can still owned by (smaller?) private groups that can compete amongst each other for users, so you basically are competing as if you were just another company in a capitalist system controlled by offer/demand and reliant on what the average consumer goes after.
This would be the equivalent of asking people to purchase ethically sourced goods and drive the market with their purchase decisions (which is actually what a capitalist system expects) as opposed to actually making laws that forbid companies from selling unethical products. That means we are not ignoring capitalism, but rather participating on it, and just asking consumers to choose ethically when they go buy a product. That's just an attempt at ethical/educated capitalism, but still capitalism.