It's a curious assortment of several different stories set in 2050, with the two big factors in the plot being the Roman Catholic church (which Blish mostly gets right) and the alien planet of Lithia, which is an oddly perfect society. It is certainly, in intellectual terms, far ahead of a lot of the sf circulating in the late 1950s.
But I think it misfires crucially on a couple of points. The first is the decision of the central character, the Jesuit Ruiz-Sanchez, that the Lithians are the direct creation of the devil. This is crucial in plot terms but (as the Pope points out to him in a later chapter) theologically very dubious. And although the presence of an alien child on Earth results in an effective and comprehensive breakdown of the human social order, I'm not completely clear on whether we are meant to think this is actually a Bad Thing; Blish's future Earth is more repressed and more debauched than ours, beyond the point where one can see it as an allegory, which means that we readers are a bit adrift as to what he is trying to say.
If the story were written today, the key character would be Cleaver, who deceives his exploratory mission colleagues, sees Lithia as a strategic military/industrial asset, returns to it to rape it of its resources, and, at the end, inadvertenty destroys it.
A Case of Conscience remains a decent effort to inject serious religious debate into the genre, but it is overshadowed by later efforts, including particularly the next Hugo winner on my list.
