do you have anything to support they did not keep the sabbath on the same day since they were shown it by GOD? or is it speculation that because they had a different calendar that they forgot which was the last sabbath they kept and what day the next sabbath would fall on? are you suggesting that isrealites changed the sabbath day to a different day? i sincerely think that would not be likely ,they may have accepted the calendar change,but their holy days including the weekly sabbath would still be kept according to the hebrew calendar but would fall on different days of the babylonian calendar much like today with the gregorian calendar, the calendar may be different but the weekly sabbath would be easily maintained based on the 6 days of work and seventh day of rest. some have tried to suggest the same idea before but its simply not true.
The Hebrew calendar is not a weekly calendar, and you might what to ask that question to the Prophet Jeremiah who wrote:
And He has violently treated His tabernacle like a garden booth; He has destroyed His appointed meeting place. The LORD has caused to be forgotten The appointed feast and sabbath in Zion, And He has despised king and priest In the indignation of His anger.
Is interesting in your attack on the Bible you continually refer to the Babylonian lunar calendar as part of your evidence.
Israel was by no means good about keeping the Sabbath.
isaiah 1:12 "When you come to appear before Me, Who requires of you this trampling of My courts ? 13 "Bring your worthless offerings no longer, Incense is an abomination to Me. New moon and sabbath, the calling of assemblies - I cannot endure iniquity and the solemn assembly.
14 "I hate your new moon festivals and your appointed feasts, They have become a burden to Me; I am weary of bearing them. 15 "So when you spread out your hands in prayer, I will hide My eyes from you; Yes, even though you multiply prayers, I will not listen. Your hands are covered with blood. 16 "Wash yourselves, make yourselves clean ; Remove the evil of your deeds from My sight . Cease to do evil, 17 Learn to do good ; Seek justice, Reprove the ruthless, Defend the orphan, Plead for the widow.
Even in the wilderness.
Ezekiel 20:10 "So I took them out of the land of Egypt and brought them into the wilderness. 11 "I gave them My statutes and informed them of My ordinances, by which, if a man observes them, he will live. 12 "Also I gave them My sabbaths to be a sign between Me and them, that they might know that I am the LORD who sanctifies them. 13 "But the house of Israel rebelled against Me in the wilderness. They did not walk in My statutes and they rejected My ordinances, by which, if a man observes them, he will live ; and My sabbaths they greatly profaned. Then I resolved to pour out My wrath on them in the wilderness, to annihilate them. 14 "But I acted for the sake of My name, that it should not be profaned in the sight of the nations, before whose sight I had brought them out. 15 "Also I swore to them in the wilderness that I would not bring them into the land which I had given them, flowing with milk and honey, which is the glory of all lands, 16 because they rejected My ordinances, and as for My statutes, they did not walk in them; they even profaned My sabbaths, for their heart continually went after their idols. 17 "Yet My eye spared them rather than destroying them, and I did not cause their annihilation in the wilderness. 18 "I said to their children in the wilderness, 'Do not walk in the statutes of your fathers or keep their ordinances or defile yourselves with their idols. 19 'I am the LORD your God ; walk in My statutes and keep My ordinances and observe them. 20 'Sanctify My sabbaths ; and they shall be a sign between Me and you, that you may know that I am the LORD your God.'