They are wrong on all counts.
Sunday was already in Apostolic times the official day of worship for Christians. Sunday worship is traditionally justified by the fact that Christ was ressurected on a Sunday. Rest assured, when Saint John received his Revelation on the Lord’s day (cf. the Apocalypse of Saint John) that he received it on a Sunday, most likely during Holy Mass, much as His Holiness, Pope Leo the XIIIth, received a private revelation about the Church while he was solemnly celebrating Holy Mass.
The fiction of Saturday-worship by Christians was invented in more modern times by the newest branch(es) of Protestantism in the 19th century to justify their sensational claims of being the reconstitution - often by divine mandate (so they say) of some sort - of the Christian Church, thus leaving everyone else from Apostolic times to their so-called church’s establishment essentially damned. It is an historically ignorant and bankrupt tactic constucted to shock Christians unfamiliar with Church History and shake them from their faith, leaving them in a Satanic doubt and uncertainity about everything they were taught about Christ and His Church. With this groundwork of uncertainty laid, the sectarians can then proceed on that premise to teach a brand new radical “Christian” theology and ecclesiology.
To put this blunty, you are being lied to. Sects like this also tend to Judaize, becoming obsessed with diet and discriminating between meats and the like. Such things are clear warning signs of a corrupted Gospel.
