I wasn't aware that the Caldari had started supporting slavery and exploiting the minmatar. I must have missed that one.
There's those missions with "slave traders" in the title where the agent says something like "they are not to be confused with the lawful slave traders we do business with on occasion who get their stock from POW's, criminals, and undesireables..." or something like that.
So there is the implication The State isn't against the existence of slavery, especially if they can do proper business with the slavers. Those who are against it bigtime would take issue with The State for that.
I've always read it so that they don't mind doing business with the Amarr etc. just because they use slaves, even when slavery is abolished in the State. So no, you can't have slaves in the State*, but they don't care if slaves are used elsewhere. Out of sight, out of mind. Of course, the corporations of low moral fibre may act rather as NIMBY - being closely affiliated with slave labour while upholding the law that there's no slaves in Caldari territory.
Of course, generalizing that to all of Caldari would mean that it would be necessary to generalize that slaves are used everywhere in New Eden. Amarr of course, Gallente criminal groups use slaves - and may have connections to Roden and other megacorporations, Minmatar are the strongest empire region for the Angel Cartel which trades slaves, and previous Caldari discussion pointing out that some Caldari may use slaves, as well - and some workers could be considered slaves, see below.
*) Low wage in obscure corporate scrip which can be used only your own stores and which cannot be exchanged except through the corporation that issued it is A-OK though. So technically freed slaves could be made to endure such an environment.
And naturally, if we take missions as something that is common and happens often, I'd very much like the Minmatar to stop trying to genocide Caldari planets with bioweapons. (This is even funnier when it happens in the Republic.) Also the licking of Gallente boots by fighting the war for them is something that does not go down well with most Caldari, I assume. In Caldari missions, the Republic is essentially a protectorate state of the Federation.