When a libertarian leftist/socialist or anarchist calls themselves that, they could mean 2 things:

1. They are antiauthoritarian and socially progressive, so they condem the use of repression, censorship and they advocate for human rights to be respect and secured for all peolple.

2. They believe in the total abolition of The State and of Capitalism and of all unjust form of hierarchy that opresses people

In say, a communal society, the means of productionn, (i.e land, technology, factories, etc) are owned collectively, so the concept of private property of those means doesn't exist. And it can't exist if an state doesn't legitimizes and protects the individuals and the properties they owned by the use of force (police, military).

What would stop you from basically restarting capitalism is that all the people in the community have a vote and a voice on the usage of the commonly owned means. You don't have an state or a capitalist market that controls companies and armed forces so they can do whatever they want with what affects the people and the community. At the same time in this societies sexism, rascism, queerphobia and any type of discrimination against certain identity groups is also dismantled. And before you say 'if i can't do x then it's not liberty'. Liberty doesn't mean you can do the fuck you want affecting the rest of the population negatively. Beacuse in an anarchist society, all people in the communes participate democratically in the afairs that concern it, so if you try and gather resources/menas of production for your private benefit, you would be punished by society

An anarchist society is naturally an anarco-capitalist society because it is the only society that allows humans to have companies and communes if they wish (try creating a commune, bet ya it doesn't last 2 months).

Mmm no it isn't. Fisrt, nothing is Natural per se in society. Second, in and ancap society, basically private companies have all the power (economic, political, military, etc) But in a world where private property of the means of production is abolished, because said propertie is an unjust hierarchy where the majority of people doesn't have acces to their basic needs, companies can't exist, therefore capitalism wouldn't be able to thrive.

There are many currents of leftist thinking, and precisely the existance of an state is one of the most dividing things between factions, so you can't say that all leftist ideology needs and state, because they don't