The emperors order:
"A Jew must not purchase a Christian slave or acquire one as a gift. If anyone disobeys this order, he shall forfeit the ownership which he wantonly obtained, and the slave shall be freed.
Jews who are adherents of a nefarious superstition may possess as property other slaves who are adherents of the true religion if those slaves were obtained as an inheritance or trust fund. They must not convert them, unwilling or willing, to pollution of their own [Jewish] sect.
If this law is violated, the criminals will suffer capital punishment and confiscation of their property." [CTh 16.9.4]
So Christians can buy other Christians as slaves, but Jews cannot buy Christians. Thus it doesn't appear as though the enslavement of Christians per se is a problem, but rather the enslavement of Christians to Jews.
The fact that Judaism is described as a "pollution" and a specific prohibition against conversion tells us why: the Roman government doesn't want to take the chance of Jews exerting too much religious influence over Christians because there's something inherently wrong with Judaism itself.