How can you be anarchists and advocates of the NAP?

As AnCaps, you advocate "let the market decide" police forces and judiciaries. But what you're really advocating for is your own normative, moral standard and constraints to be imposed on the market for law; specifically, the nonaggression principle. If you let a market decide how retaliatory force should be used, minorities with different views can unilaterally form their own police forces if enough people are willing to pay. For example, there's the anti-abortionists who try and execute certain doctors for their crimes against the "unborn", the Leftists who forcibly regulate or break up businesses for the “crime” of seeking profits, and the Islamists who form their own police forces to enforce Sharia Law.

In response to these illiberal agencies, can the police that fully support individual rights ban and forcibly disband competition on the grounds that they enforce unjust laws by unjust means? If so, then you cease being anarchists - these agencies jointly constitute one complex institution with a monopoly on the use of force—a government. If they cannot forcibly disband other agencies on pain of "restricting competition", then libertarian anarchy is incompatible with the NAP, because it unleashes brute force and injustice.