Exodus 20
8Remember the sabbath day, to keep it holy.
9Six days shalt thou labour, and do all thy work:
10But the seventh day is the sabbath of the LORD thy God: in it thou shalt not do any work, thou, nor thy son, nor thy daughter, thy manservant, nor thy maidservant, nor thy cattle, nor thy stranger that is within thy gates:
11For in six days the LORD made heaven and earth, the sea, and all that in them is, and rested the seventh day: wherefore the LORD blessed the sabbath day, and hallowed it.
When I look at the fourth commandment, restated again in Deuteronomy 5, the focus is not on "commerce" objectively. It seems the focus is on you, as one of God's people to rest from work, and the ordinary self-preoccupations of the rest of the week, and give yourself, in priority, to worship Him all the day. This is thought, word, and deed.
The corollary of this, necessarily related to it is you ought not by your actions prevent others from doing the same.
Christ explicitly explains in the application of this glorious commandment, allowance for for works of necessity and mercy and Scripture implicitly allows the church to operate and do its "job" (sometimes called piety).
So, if a church's job is teaching and preaching the Word of God, we might assume literature distribution is part of that, from the church's standpoint. This is not the kind of "work" the commandment is prohibiting. Not things that are necessarily and incidentally related to the church during her "work" on the Lord's Day.
Even commerce is not absolutely prohibited in that commerce that involves mercy or necessity is (generously) allowed. An example of this would be if you were sick, you could buy medicine, even though you pay money for it and are causing somebody to work to provide it. God has graciously chosen not to place undue burden on us. Rather, He exhorts us to call the sabbath a delight.
It would seem to me to be a more difficult case to invite in an outsider to the church to sell his own materials at the church, but that's not quite the same case as the church doing its ordinary sabbath "job."
The more I think about this, the commandment would allow the church to disseminate Christian literature, even charge for it. There are time, manner and place restrictions to prevent undue distraction or causing unbelievers or weak believers not to stumble. They must be considered.
Churches may wisely choose just not to deal with the other considerations and not collect money for any materials, but now, after considering all these good posts and the Scripture, I don't think the fourth commandment or any other biblical precept strictly prohibits it.
(I'm suprised to come to this conclusion)
