One thing that is not always taken into consideration about Sabbath-keepers is that keeping the Sabbath and being under the New Covenant don't have to be mutually exclusive.
I am saved by grace through faith in my Savior who died in my place. Because of that sacrifice, I am made clean before Him and my sin is forgiven. His Spirit dwells in me and leads me to live how God sees fit. (For the sake of this post, this is a very basic understanding of the New Covenant.)
But God has called us to be His children, bride. priests, ambassadors, apostles, messengers, etc. We live a life by His leading to further His Kingdom. As a response to the grace shown me, I want every part of my life to be honoring to Him. Me keeping the Sabbath as a weekly rest does not impede or nullify that grace . If I were keeping the Sabbath as a means to impress God or seek favor or justification, then I would be out of order (and some folks do that.) My obedience to any other aspect of the Law is similar. I am under no curse of the Law because of my Savior, so even if I keep it imperfectly, I am not punished. What the Sabbath and other aspects of the Law does is show me practical ways to live a life worthy of the calling given to me. I believe these commands are valid and still applicable for all Christians, just in proper relationship to grace.
While there are some who use the Law inappropriately, not all do. And again, the 2 don't have to be mutually exclusive.