Must Christians obey the Old Testament?

[useful idiot]

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That has nothing to do with the moral law. Those are the only ritual laws that the church has to obey. The disagreement that led to the Jerusalem Council was over circumcision, not whether you can lie or murder.

There's only one aspect of the OT law that is still in effect for the church and that's the moral aspect, not the ceremonial or judicial. Obviously that above statement from Acts does away with ceremony and the judicial laws have no bearing because God isn't working through national Israel during this "dispensation".

[useful idiot]

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That has nothing to do with the moral law. Those are the only ritual laws that the church has to obey. The disagreement that led to the Jerusalem Council was over circumcision, not whether you can lie or murder.

There's only one aspect of the OT law that is still in effect for the church and that's the moral aspect, not the ceremonial or judicial. Obviously that above statement from Acts does away with ceremony and the judicial laws have no bearing because God isn't working through national Israel during this "dispensation".

But the question becomes where to the ritual laws end and the moral laws begin?  Is keeping the Sabbath a ritual law or a moral one, for example?

Good Christians have disagreed about the Sabbath. The confession that I have generally pointed to in the past as a good exposition of my beliefs, The London Baptist Confession of 1689, affirms sabbatarianism, however I do not. I think it's ceremonial. I think that the fact that early church celebrated the first day of the week as the Lord's Day, without any major fuss being made about it indicates as much. Paul in Colossians 2:16 says "Therefore no one is to act as your judge in regard to food or drink or in respect to a festival or a new moon or a Sabbath day".

As for other laws, I think you can clearly see where a moral principle is involved in the Mosaic Law and distinguish it from something ceremonial. Let's take two verses from Leviticus 18:

"Do not have sexual relations with your brother's wife; that would dishonor your brother"

"Do not approach a woman to have sexual relations during the uncleanness of her monthly period"

Obviously one is moral, the other ceremonial. If I were to have sexual relations with my brothers wife, then I would be breaking God's law. If I were to have sex with my wife who was menstruating, I wouldn't be.

Given the fact that the judicial aspect passed away with national Israel, we are largely left with the Spirit to guide us in these matters. Hence why I can disagree with someone about working on Sunday, and no one is going to get executed over it. Jmfcst wrote earlier about God's commands to Noah in Genesis 9. There is one legal principle that God established over the whole world, that of capital punishment in response to someone taking another's life. This principle is applicable and clearly re-iterated in the New Testament. Even if it weren't reiterated, it is still binding because it's not part of the Mosaic Law...

[useful idiot]

So you are saying God lied about the seventh day being perpetually ordained as the sabbath?

I could see the argument that the perpetual covenant to follow the seventh-day sabbath laid out by God in Exodus 31:12-17 applies not to the Gentiles, but only to the Jews, as an obligation of their status as his "kingdom of priests" (Exodus 19:6), but holding such a distinction between Jew and Gentile would be at odds with the structural supersessionism you espouse.

The NT reads the OT Christologically. If that's supersessionism then the NT is a supersessionist document. Jmfcst alluded to it, but let's look at the next verse

 "It is a sign between Me and the sons of Israel forever; for in six days the LORD made heaven and earth, but on the seventh day He ceased from labor, and was refreshed." (Ex. 31:17 NASB)

In its context the passage is speaking of the Sabbath as something holy only because of its significance, not because it's holy in and of itself. It's made clear from the context WITHIN the OT that it is symbolic. It's perfectly within God's right to change the mode of how that symbolism is expressed.

If you accept the fact that both the NT and OT are of God then there is no contradiction there. This is a matter of presuppositions. If you don't accept the authority of the NT you're going to see contradictions, and if you do accept it then you won't.