In an anarcho capitalist society, all law will be what was known in medieval times as private law.
This unavoidably has the effect that in general people will not be altogether equal before the law.
In medieval times, access to the market in defence and arbitration services was severely unequal, because of the severely oligopolistic nature of that market, and as a result private law treated people grossly unequally. Thus the phrase “private law” became “privilege” (“privy lege”)
I would expect that in a genuinely free market for defence and justice, private law would be fairly uniform, resulting in rough equality before the law in all important matters, other than the normal inequality that protects the rich man's estate equally with the poor man's shirt, and forbids rich and poor alike to sleep under bridges, or at any rate near enough equal that few people would feel like fighting over it.
This reflects the fact that a rich man's estate is subject to greater threats, in proportion to his ability to pay for defence against those threats. Indeed since a rich man is less capable of himself defending his property than a poor man, it is likely that rights to property directly under the control of the owner would be privileged relative to less direct forms of ownership. It is less expensive, and therefore more profitable, to defend one hundred small properties owned and defended by one hundred men, than to defend one large property owned, but not defended, by one man.
But suppose for example, the members of “The Old Hippy Militia”, felt that adultery should not be subject to violent reprisals, and the clients of “Gods Soldier's” felt that it should.
In that case the “Old Hippy Militia” and the “God's Soldiers” would very likely come to an agreement that resulted in inequality before the law between a member of “The Old Hippy Militia” who committed adultery and a client of “God's Soldiers” who committed adultery.
The following notice might appear in the sign up agreement for people signing up with the “Old Hippy Militia”
“In the event that you are killed or injured by a husband while you are impregnating that husbands wife: the Militia undertakes to avenge you, (after due process) unless the marriage contract was registered with one of the following contract enforcement agencies […], or the husband is a member or client of one of the following militias or defence agencies […]”
And the following notice might appear in the “God's soldiers” notification:
“In the event that you are killed or injured by a husband while you are impregnating that husbands wife: may God have mercy on your soul. Your right to protection shall be canceled from the date of the adultery.”
And if “God's Soldiers” succeeded in getting enough defence organizations to agree to tolerate their practices, then a rich man marrying a young wife might well prefer to have his marital contract registered with “God's soldiers” even though he has all his other contracts registered with “Dun and Bradstreet” On the other hand, perhaps he might not. Possibly his wife might not.