Liberalism does effectively require some framework for private ownership, but that in itself is not a sufficient condition for Capitalism. My issue with what you are saying is the conjecture that you cannot have socialist economic structures alongside liberal political ones, which is the (incorrect) dogma of many online leftist spaces. You can have collective ownership of labor (in various forms), while still owning a house or a suitcase or a jacket, while also being an actualized participant in liberal democracy.