Yes and they believe we deliberately sin by worshiping on Sunday. However there is no verse in the in the New Testament the restated KEEP THE SABBATH.
Look who is supposed to KEEP THE SABBATH:
Exodus 31:12-18 (HCSB)
12 The LORD said to Moses:
13 “Tell the Israelites: You must observe My Sabbaths, for it is a sign between Me and you throughout your generations, so that you will know that I am Yahweh who sets you apart.
14 Observe the Sabbath, for it is holy to you. Whoever profanes it must be put to death. If anyone does work on it, that person must be cut off from his people.
15 Work may be done for six days, but on the seventh day there must be a Sabbath of complete rest, dedicated to the LORD. Anyone who does work on the Sabbath day must be put to death.
16 The Israelites must observe the Sabbath, celebrating it throughout their generations as a perpetual covenant.
17 It is a sign forever between Me and the Israelites, for in six days the LORD made the heavens and the earth, but on the seventh day He rested and was refreshed.”
18 When He finished speaking with Moses on Mount Sinai, He gave him the two tablets of the testimony, stone tablets inscribed by the finger of God.
Now lets Look at the Commands pertaining to worship in the New Testament:
Romans 14:5-12 (HCSB)
5 One person considers one day to be above another day. Someone else considers every day to be the same. Each one must be fully convinced in his own mind.
6 Whoever observes the day, observes it for the honor of the Lord. Whoever eats, eats for the Lord, since he gives thanks to God; and whoever does not eat, it is for the Lord that he does not eat ⌊it⌋, yet he thanks God.
7 For none of us lives to himself, and no one dies to himself.
8 If we live, we live for the Lord; and if we die, we die for the Lord. Therefore, whether we live or die, we belong to the Lord.
9 Christ died and came to life for this: that He might rule over both the dead and the living.
10 But you, why do you criticize your brother? Or you, why do you look down on your brother? For we will all stand before the tribunal of God.
11 For it is written: As I live, says the Lord, every knee will bow to Me, and every tongue will give praise to God.
12 So then, each of us will give an account of himself to God.
There is no condemnation in VERSE 5. Yes they are allowed to worship on Saturday, but that does not make them more Holy, and if Pride wells up, that Pride is sin, and does not earn us SALVATION. Likewise, I do believe one who believes every Day is alike, as I think I should Believe my attitude Toward Christ, should be Not be less than any other Day. Sure I worship on Sunday, but I talk to the LORD every day.
Here is our Worship COMMAND, notice there is not specific day mentioned:
Hebrews 10:19-25 (HCSB)
19 Therefore, brothers, since we have boldness to enter the sanctuary through the blood of Jesus,
20 by a new and living way He has opened for us through the curtain (that is, His flesh),
21 and since we have a great high priest over the house of God,
22 let us draw near with a true heart in full assurance of faith, our hearts sprinkled ⌊clean⌋ from an evil conscience and our bodies washed in pure water.
23 Let us hold on to the confession of our hope without wavering, for He who promised is faithful.
24 And let us be concerned about one another in order to promote love and good works,
25 not staying away from our ⌊worship⌋ meetings, as some habitually do, but encouraging each other, and all the more as you see the day (the Rapture) drawing near.
And these Verses:
Ephesians 5:17-20 (ASV)
17 Wherefore be ye not foolish, but understand what the will of the Lord is.
18 And be not drunken with wine, wherein is riot, but be filled with the Spirit;
19 speaking one to another in psalms and hymns and spiritual songs, singing and making melody with your heart to the Lord;
20 giving thanks always for all things in the name of our Lord Jesus Christ to God, even the Father;