In either case, your objection is the standard objection to anarchy, that supposedly nothing prevents people from hiring a criminal gang instead of a protection firm. There is nothing in your objection that is specific to abortion. You could just as easily said that I can hire goons to do my murdering, then choose judges that believe in murder.
The question is, is independent and competent adjudication possible in the environment where multiple independent law enforcers exist? I haven't read the book, but I don't see why not. Here is
Annalex-Hoppe Theorem. In a multiple law enforcer environment, independent judiciary will reflect the community standard of justice.
Indeed, if a judge consistently allows verdicts that do not reflect the community standard of justice, a coalition of enforcers will form against him, and it will be stronger than a coalition of enforcers in his defense.
So, in a way, you are right that pro-abortion verdicts are possible under a multiple enforcer system, if the community standard of justice is pro-abortion (or pro-murder, pro-credit card fraud, etc), but that is no different from a single enforcer system that we have now.
You're right. My objection is that in practice there'd be no way to avoid violent chaos. Abortion is one of the things that will lead to it (or else go unpunished altogether).
Annalex-Hoppe Theorem. In a multiple law enforcer environment, independent judiciary will reflect the community standard of justice.
In the case of abortion (and, no doubt, other issues) there is no community standard. You'd have to have such a standard formed and the exclusion of "wildcards" already in place before you can hope to have a decently functioning anarchist society, and I just don't see that happening. And if it does happen, it could be undone by any number of factors.