They work. I don't want to work Christmas, Sundays, Easter etc for religious reasons, but that doesn't fly either. The sabbath (assuming that is the argument) is sacred for many, however there are biblical provisions for people in our situation caring for others. As long as a sabbath is observed it need not be on a particular day.
If you give them all Saturdays completely off we would need a different person to cover, so 3 on per weekend instead of 2 (Sunday is backup Saturday). It could be done at great expense I suppose, but I think it would cause major issues in a small group.