Consider Exodus 20:8
Remember the Sabbath day to keep it holy. (NASB)
Holy means “devoted to G-d” (Merriam Webster’s Collegiate Dictionary). How are we devoting the Sabbath (or any day for that matter) to G-d?
Tell the people of Isra'el, "You are to observe my Shabbats; for this is a sign between me and you through all your generations...because it is set apart for you. (CJB)
Separate means "to set apart; to differentiate between"
[You are] to keep the Shabbat, to observe the Shabbat...as a perpetual covenant. (CJB)
G-d's word says that the Sabbath is a holy day. In Isaiah 58:13-14, it basically tells us not to pursue our own interests. We are to honor the day by not doing our usual things or speaking about them (such as school, work, sports, etc). In Isaiah 56:1-2, the Word tells us that happy is the person who keeps the Sabbath and keeps himself from evil.
We know the foreigners also celebrated the Sabbath not just Israel. In Isaiah 56:6, it tells us that the foreigners joined themselves to G-d because they wanted to serve him. It also states that if the foreigners would serve him, love the name of Adonai, be his workers, and hold fast to his covenant, then He would bring them to his holy mountain and make them joyful in his house of prayer and that their prayers would be accepted on his altar.
In Hebrews 4:9-11, the Word tells us that a Sabbath rest is for all the people of G-d. Does this mean for all the people of G-d? I think so. G-d wants us to understand the Sabbath now because we will celebrate Sabbath with Him in the world to come. Isaiah 66:23 tells us that every week on Shabbat, everyone will come to worship in G-d's presence. This is speaking of the world to come.
In Ezekiel 20:12, G-d tells Ezekiel that He gave the Sabbath as a sign between us and him so that we would know He is the only one who can make us holy.
In Matthew 12:8, He tells us that the Son of Man (Yeshua) is Lord of the Sabbath.
In Nehemiah 10:32 the men of his day made a binding covenant stating "we will not buy... on Shabbat or on a holy day." (CJB)
Even in his time, (Nehemiah 13) Ezra saw people working on Shabbat and bringing items to Jerusalem to sell. He asked them "What is this terrible thing you are doing, profaning the day of Shabbat? Didn't your ancestors do this...?" Have we not learned from their mistakes? We need to realize that Shabbat is an island in time....a time that is set apart from all other days! It is a special and holy day and we need to be careful in what we do. Are we doing what G-d wants us to do?
Not honoring the Sabbath
G-d explains to Ezekiel that Israel had profaned the Sabbath because of their idolatry. When they would go and sacrifice their children on the Sabbath they would then go to the Temple on the same day. G-d was upset with Israel because they were not honoring the Sabbath.
G-d does not change
G-d did not ever change the Sabbath day. In Malachi 3: 6, He tells us "I, Adonai, do not change."
The Lord's Day
The only passage in Scripture that mentions "the Lord's Day" is found in Revelation 1:10 when John has visions of things to come. Throughout Scripture the Sabbath is never changed from Saturday to Sunday. Since Yeshua is the "Lord of the Sabbath" then "the Lord's Day" refers to the weekly Sabbath.
Should we not hear and observe what G-d has commanded rather than make up our own special days?