I'm afraid a lot of Christians -- Latin, Protestant, and Orthodox alike -- labor under the delusion that Our Lord's injunction "In as much as ye do it to the least of these, ye do it unto me" somehow makes it spiritually beneficial to support government-run programs to succor the poor out of tax revenues. Strangely, observing the baleful effects of such programs in practice, does not seem to convince them otherwise.
You have captured much of the problem right here. Morphing the words of Jesus has been the, pardon me, lame excuse for backing perceived champions of a State-run welfare system. They now have more baggage than they bargained for.