if we take as a given the origin story of superman--last survivor of another world dropped surreptitiously and raised the same in our world who makes his appearance as an adult--I think the reaction of most religious institutions to his existence would be denial of it or alternatively deification of him. xianity, especially, would react to superman as a rival to jesus, perhaps even seeing him as the antichrist, although it's just as possible he would be seen as the second coming. but the primary reaction I think would be that he is an affront to god since he would be, at least the way he's presented in original stories, a near-perfect being. for the same reason, I suspect institutional islam would denounce him (tho I also think sufiism would be drawn to him).
judaism might see him differently and might even recognize superman as the messiah. I'm not certain what the reactions of other religions like hinduism or buddhism might be (although this is an interesting take) but I think that the raelians and scientologists as well as other alien-based faiths would welcome him, not as an adherent but as the focus of worship or at least as an emissary.
likewise, I don't think he would be likely to identify exclusively with a single nation or social group like the white americans he's mostly surrounded by in comics. particularly if he were seen as some emissary or agent of god I suspect people would expect him to effect god's will by counteracting disasters that are also seen as "god's will" such as earthquakes, hurricanes, and tsunamis or other impersonal forces like disease and war. as a result he would have neither the time or need for a secret identity.