Hebrews 4:9-11 9 There remains, then, a Sabbath-rest for the people of God; 10 for anyone who enters God’s rest also rests from their works, just as God did from his (If you're doing it just as God did from his, then are you not doing it on a Saturday? Because to do it on a Sunday would not be doing it just as God did, which goes back to picking and choosing). 11 Let us, therefore, make every effort to enter that rest, so that no one will perish by following their example of disobedience.
The sabbath in the OT was a lesson and a sign between God and Israel..not God and the church.
And on that note, I don't see how you don't think a day of rest holds any religious value. If that's what you think, then you've missed God's point. God's reason for a Sabbath was never to give man a break from a hard week at work lol. God wasn't trying to be nice. His reason for the Sabbath was so that on that day, man could stop all he was doing long enough to honor God and all he had done...and I think that holds tons of religious value, don't you?
...but I'm not particularly religious, I just don't see how a religious person could not see value in making sure one takes enough time to give praise to the God they hold so dear.