"God has never required that non-Israelites keep certain Laws which were given to separate Israel from the nations. God required Israel to circumcise their males on the eighth day to set Israelites apart as a covenant people. God required Israelites to observe the seventh-day Sabbath as a sign between him and Israel forever. God required Israelites to wear fringes on their garments as markers of their identity. God required Israelites to make a pilgrimage three times a year to Jerusalem, but certainly didn’t expect Gentiles to do so. God required Israel to restrict its diet of meat to certain species and to avoid accidentally killed animals. God did not forbid, but allowed non-slaughtered meat to be sold to Gentiles." (http://derek4messiah.wordpress.com/2010/05/11/expositing-acts-15-the-defining-chapter/)
So by this reasoning then, if a Gentile decides to keep the Sabbath, he's hurting Israel's distinctiveness.
It's interesting though that Paul had no problem with the Colossians observing Shabbat. He told the Gentile Believers at Colossae to keep Shabbat (etc) even despite the harsh judgments they were receiving from ascetics (people who shunned any sort of pleasure). Paul didn't say anything about how Gentile observance of Shabbat would injure Israel's distinctiveness.
The truth is that G-d's plan has always been for Gentiles to celebrate Shabbat and bring them to His Temple (Isaiah 56).
But isn't Shabbat a sign of the Sinaitic Covenant?
"16 The Israelites are to observe the Sabbath, celebrating it for the generations to come as a lasting covenant. 17 It will be a sign between me and the Israelites forever, for in six days the LORD made the heavens and the earth, and on the seventh day he abstained from work and rested." (Exodus 31:16-17)
"12 "Observe the Sabbath day by keeping it holy, as the LORD your God has commanded you. 13 Six days you shall labor and do all your work, 14 but the seventh day is a Sabbath to the LORD your God. On it you shall not do any work, neither you, nor your son or daughter, nor your manservant or maidservant, nor your ox, your donkey or any of your animals, nor the alien within your gates, so that your manservant and maidservant may rest, as you do. 15 Remember that you were slaves in Egypt and that the LORD your God brought you out of there with a mighty hand and an outstretched arm. THEREFORE the LORD your God has commanded you to observe the Sabbath day." (Deuteronomy 5:12-15)
So it's absolutely a sign of the Sinaitic Covenant.
We also know that G-d wants His Temple to be a House of Prayer for all people and that He won't let anyone enter the Temple who is uncircumcised in the flesh (Isaiah 56:7 and Ezekiel 44:9).
So G-d wants Gentiles to observe the sign commandments of the Sinaitic Covenant.
Now, keep in mind, that Gentiles are included in the covenant through Yeshua and that things like circumicision are mere "signs". So here's some logic for you: if a Gentile should receive circumcision as a sign that he is covenanted then should he not also wear tzitit, etc? Should he not manifest all the other "signs" of being covenanted? Is it not his right (and duty) as a covenantal member to take upon himself those signs?