Many anti-Sabbatarians argue that we don't have to keep the Sabbath and dietary laws because the old covenant has passed away. Hebrews 8:13 says that the old covenant "is obsolete and growing old will soon disappear" (NRSV). And Hebrews 8:18-20 traces this covenant to God's revelation to Israel at Mount Sinai. So one anti-Sabbatarian argument runs like this:
Premise 1: The old covenant is now obsolete.
Premise 2: The old covenant was made at Sinai, when God gave his Torah to Israel.
Premise 3: This Torah is now obsolete because the old covenant has passed away.
Premise 4: The Torah contained the Sabbath and dietary laws.
Conclusion: The Sabbath and dietary laws are now obsolete, since they were part of the old covenant at Sinai, which has passed away.
Sabbatarians respond that many of these laws existed before the old covenant at Sinai, so the dissolution of the old covenant does not imply their abolition. As Ron Dart (of the Armstrongite tradition) has asked, "How can the passing away of the old covenant destroy what the old covenant did not create in the first place" (my paraphrase)? And Seventh-Day Adventists have argued that the Sabbath and dietary laws pre-dated Sinai, so they are binding on Christians today. For SDA's, the laws made at Sinai (e.g., the annual holy days, the Levitical priesthood) presumably are not obligatory, since they were God's "ceremonial law" for Israel, not all humanity. But the pre-Sinaitic laws are for all people.
Adventists apply this reasoning to the dietary laws of Leviticus 11. In Genesis 7:2, God says to Noah, "Take with you seven pairs of all clean animals, the male and its mate; and a pair of the animals that are not clean, the male and its mate[.]" According to many Sabbatarians, this shows that the distinction between clean and unclean meats pre-dated Mount Sinai. Therefore, in their minds, it represents God's will for all of humanity, and it is binding on Christians today.
I can somewhat understand why Sabbatarians contend that pre-Sinaitic laws are authoritative. In Mark 10:6-9, Jesus appeals to God's law at creation to argue that divorce is not an option. He basically dismisses the law of Moses on the topic, claiming that it only allowed divorce because of the Israelites' hardness of heart (v 5). But he sees something authoritative in God's commandment at creation. And Paul upholds Jesus' ruling (I Corinthians 7:10).
But where the pre-Sinaitic argument falls short is here: there is at least one pre-Sinaitic institutions that Christians don't have to do: animal sacrifices. Noah had to take seven clean animals onto the ark for sacrifices (Genesis 8:20), a practice that goes back to Cain and Abel (Genesis 4). Yet, Hebrews 9-10 is clear that Christians don't have to sacrifice animals.
And that applies to some other institutions that pre-dated Sinai. For example, Abraham had to be circumcised (Genesis 17). Yet, Acts 15 and Galatians state that Gentiles don't have to do this.
Colossians 2:16 says that the Jews' rules on eating and drinking were a shadow of things to come, yet their substance is Christ. Maybe God tried before his revelation at Sinai to foreshadow what Jesus would do. He was preparing people as early as Noah's day to discriminate between clean and unclean when they offered an animal to God. Today, however, Christians don't need to rely on such a physical ordinance, for our discrimination is primarily moral (Matthew 7:18-23). Plus, Christ has been offered on our behalf, and he is definitely a "clean" sacrifice, morally speaking! Likewise, the Old Testament required Israelites to offer sacrifices that were without blemish, and the New Testament applies that to Christ's moral and spiritual perfection (Hebrews 9:14; I Peter 1:19). Can we interpret Noah's sacrifice of clean animals in a similar way: that they foreshadowed Christ's conformity to God's standards? Can we apply the distinction between clean and unclean in a spiritual sense, not necessarily literally?
Also, could it be that, prior to Sinai, God did certain things with Israel's election in mind? When God commanded Noah to distinguish between clean and unclean animals, he was telling him that God only eats animals that conform to a particular standard. But, later on, Israel would imitate God's diet when she rejected unclean foods in favor of what's kosher (Leviticus 11), the same way that she followed God's example by resting on the Sabbath day (Exodus 20:8-11; 31:17). The Gentiles didn't follow such dietary laws, for God told Noah that "[e]very moving thing that lives shall be food for you" (Genesis 9:3). But Israel was special--she was separate, or holy. Other nations could eat whatever they wanted (provided they slaughtered it properly), but Israel had to share God's dietary restrictions by limiting themselves to clean animals. It was a sign of her chosen status. And Leviticus 11 twice says, "[Y]ou shall be holy, for I am holy" (vv 44-45). Perhaps God planned his diet with Israel's later election in mind!
But those were the days when God relied on physical ordinances to make his point! He doesn't use animal sacrifices now that Jesus has come. Maybe the kosher laws also had a temporary purpose: to foreshadow Christ and to highlight Israel's election.