The problem with this conspiracy theory is that Christians were keeping the Lord's day "Sunday" while they were being slaughtered by the pagan Romans. All through the early centuries the Christians were hiding in the catacombs keeping the "Lord's day". Long before Constantine was a twinkle in his father's eye the Christians were keeping the Lord's day.
Unfortunately however people would rather believe the rantings of pseudo-christians sects and cults than the writings of the ante-Nicene fathers. You would think that the church had never written on the subject before the Council of Laeodica the way these crackpots rave.
Canon 29 correctly reflects Christian teaching of centuries prior by saying
On the Lord's own day, assemble in common to break bread and offer thanks, but first confess your sins so that your sacrifice may be pure."
Didache, 14 (A.D. 90).
"If, therefore, those who were brought up in the ancient order of things have come to the possession of a new hope, no longer observing the Sabbath, but living in the observance of the Lord's Day, on which also our life has sprung up again by Him and by His death--whom some deny, by which mystery we have obtained faith, and therefore endure, that we may be found the disciples of Jesus Christ, our only Master."
Ignatius, To the Magnesians, 9:1 (A.D. 110).
"The seventh day, therefore, is proclaimed a rest--abstraction from ills--preparing for the Primal Day,[The Lord's Day] our true rest; which, in truth, is the first creation of light, in which all things are viewed and possessed. From this day the first wisdom and knowledge illuminate us. For the light of truth--a light true, casting no shadow, is the Spirit of God indivisibly divided to all, who are sanctified by faith, holding the place of a luminary, in order to the knowledge of real existences. By following Him, therefore, through our whole life, we become impossible; and this is to rest."
Clement of Alexandria, Stromata, 6:16 (A.D. 202).
"The apostles further appointed: On the first day of the week let there be service, and the reading of the Holy Scriptures, and the oblation: because on the first day of the week our Lord rose from the lace of the dead and on the first day of the week He arose upon the world, and on the first day of the week He ascended up to heaven, and on the first day of the week He will appear at last with the angels of heaven."
Teaching of the Apostles, 2 (A.D. 225).
"Hence it is not possible that the rest after the Sabbath should have come into existence from the seventh of our God; on the contrary, it is our Saviour who, after the pattern of His own rest, caused us to be made in the likeness of His death, and hence also of His resurrection."
Origen, Commentary on John, 2:27 (A.D. 229).
"On the seventh day He rested from all His works, and blessed it, and sanctified it. On the former day we are accustomed to fast rigorously, that on the Lord's day we may go forth to our bread with giving of thanks. And let the parasceve become a rigorous fast, lest we should appear to observe any Sabbath with the Jews, which Christ Himself, the Lord of the Sabbath, says by His prophets that 'His soul hateth;' which Sabbath He in His body abolished."
Victorinus, On the Creation of the World (A.D. 300).
"They did not care about circumcision of the body, neither do we. They did not care about observing Sabbaths, nor do we."
Eusebius, Church History, 1:4,8 (A.D. 312).
"Also that day which is holy and blessed in everything, which possesses the name of Christ, namely the Lord's day, having risen upon us on the fourth of Pharmuthi (Mar. 30), let us afterwards keep the holy feast of Pentecost."
Athanasius, Epistle 9:11 (A.D. 335).
"Fall not away either into the sect of the Samaritans, or into Judaism: for Jesus Christ henceforth hath ransomed thee. Stand aloof from all observance of Sabbaths, and from calling any indifferent meats common or unclean."
Cyril of Jerusalem, Catechetical Lectures, 4:37 (A.D. 350).
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So you see the Council of Laodecia correctly reflects the practice and teachings of Christians for the preceeding centuries.
Canon 29
Christians must not judaize by resting on the
Sabbath, but must work on that day, ratherhonouring the
Lord's Day; and, if they can, resting then as
Christians. But if any shall be found to be judaizers, let them be
anathema from Christ.
Sadly however the Judaisers are still with us to their great shame.
Let them be anathema from Christ.