It's not so cut and dried. Statism and anarchy are not the two Boolean options, nor really is it a linear spectrum between them. These just happen to be the two most pitted against each other in these circles.

Localism puts power together with vicinity. The closer you are to something, the more authority you ought to have, including the most fundamental unit: the person.

A father properly leading his family is not statism. Sure, the opportunity for tyranny exists, as it does on every level of society, but his proper exercise of authority does not make him a tyrant.

The community can collectively decide to exclude a member if that member is in violation of others, such as a family of criminals, or mafia, can be legitimately ejected from a neighborhood. That is not statism, but the local people making decisions that are best for it. They can even collectively decide to appoint an individual to carry out such work for the good of the community and its members: in a word, a sheriff.

Statism itself is the view that the state is the source of authority, or that its authority is absolute, and anarchy is the denial that any authority is legitimate. Localism is the balanced understanding that authority does indeed exist, is legitimate, and ought to be held in as low a level as possible to achieve an end.

To illustrate, take sustenance. A family is rightfully concerned about each individual's food. The community ought not be concerned of a single individual's food, but it ought to be of whole families. A city ought not be concerned with a single family's food, but it ought concern itself with whole communities. The state ought not concern itself with a single community's food, but it ought to of whole cities. You get the picture.

Tyranny occurs when a higher authority concerns itself with a lower matter than is appropriate, and that is not limited to the state alone, or even the city. Localism puts that authority in the appropriate hands.