There are some groups (most notably the Seventh Day Adventists) who argue that Saturday is the only proper day of worship, even in the New Covenant. While this is not a debate I have invested much time in (very few Sabbath-Keepers in Ireland) I don't find it to be a hot button issue for me in comparison to other central issues (e.g., Christology). Notwithstanding, as it is a move lively debate in the USA and elsewhere, here are some resources on the issue that I think would be interesting for both LDS and non-LDS who interact with such dogmatism vis-a-vis the "proper" day of worship (while most LDS celebrate church on Sundays, this is not a dogma; in the UAE, for instance, church is celebrated on Fridays, so there are some geographical considerations).
D.A. Carson, ed. From Sabbath to Lord's Day: A Biblical, Historical, and Theological Investigation
Anthony F. Buzzard, The Law, the Sabbath, and New Covenant Christianity (pdf)
The Lord's Day by B.H. Roberts (pdf)
D.A. Carson, ed. From Sabbath to Lord's Day: A Biblical, Historical, and Theological Investigation
Anthony F. Buzzard, The Law, the Sabbath, and New Covenant Christianity (pdf)
The Lord's Day by B.H. Roberts (pdf)
