Attempts will still be made to enforce what people think ought to be laws. Those attempts will be viewed as crimes by others, who will try to act on that perception.
I can tell you how it is worse. Now a single law enforcer, the state, is combined with hierarchical judiciary. Thus we have our Supreme Court Commissars ensuring a sclerosis of the community. In fact, we barely know what the community standard is on abortion. The pro-abortion folks tell us that the point is not worth arguing because the Supreme Court already decided the issue. The pro-life folks point out that while there is no consensus on banning abortion, there is a consensus on banning partial birth abortions, parental notification and welfare abortions, and each time the court is to the left of the consensus. I'd much rather have chaos (another word for which is local control).
Violent chaos doesn't mean local control, it means lots of factions shooting at each other.
There is largely a consensus on things like partial birth abortion, but not on abortion as abortion. Both of these facts come from the same source, polls, so you can't accept one and reject the other.
In the abortion controversy, we have too much shooting to my taste already. Attempts are made to enforce what people think ought to be laws. Those attempts are viewed as crimes by others, who act on that perception.
Yours seems to be the vulgar critique of anarchism as "people shooting at each other". In fact, any law is enforced by a balance of power, where most people know how to avoid a shootout. With a single enforcer most people know that if they rob a bank, a shootout will ensue. They decide not to rob banks. With multiple enforcers, most people will know how to avoid a shootout as well, and when a conflict of interpretation of natural law presents itself, they would prefer to submit to a judge. When a recalcitrant party refuses adjudication, that party would face a coalition consisting not only of its opponents in the controversy on hand, but also of its former allies. For example, those who shoot abortionists are condemned not only by pro-abortion people, but by the overwhelming number of pro-life people.