I was gonna disagree, but I couldn’t actually think of a functioning stateless ideology which allows private property. Anarchism is inherently for abolishing private property, so that’s out already. That mostly just leaves you with "anarcho-"capitalism which is just replacing the government with an ultra-capitalist power structure and decimating social mobility, it’s just an undemocratic state but shittier…
The recent EU elections are a pretty good reminder of this