I definitely think that there would be problems with free market defense agencies, but what it comes down to, as I see it, is companies will hold their workers, the enforcers, more accountable than the state holds its police accountable.
When a police officer paid by the state guns down children, dogs, and old people, they get paid leave. If an enforcement agent in a company does this, the company runs the risk of losing customers. Therefore companies will hold their workers accountable. Without any state to protect the companies, there is a sensitive budget involved and any mess-ups could leave the company owner in a bad position.
I would argue that the companies are not states because the state has a monopoly on violence, while agencies are limited by other agencies and arbitrators. I would also argue that the minority has a better chance of being well represented by law enforcement than in our current system. In a democracy, the minority always loses. In a free market, the poor don't compete with subsidies or government-funded monopolies of any kind. Any one poor guy in the neighborhood could pick up a gun and earn money or food by protecting people and guarding the neighborhood (I'm aware this could go terribly wrong too).
And as for those who do not participate in the capitalist realm, who are in separate communities... Of course, there will be a clash. What does the anarcho-communist do when the anarcho-capitalist infringes on their rights? Only the capitalist has a defense agency. I suppose the communist would expect their friends to help or something, but I can't imagine that working out too well. I think this is something I can't answer and would like to have a discussion on.