Chris Keller certainly sees himself as an idealist. His wartime experiences have given him a firm sense of right and wrong, and he finds it somewhat frustrating that such a black and white view of the world isn't widely shared in civilian life. The suggestion here is that Chris's idealism is steeped in naivety. Though Chris must have witnessed a lot of death and suffering during his wartime service, at no point was his simplistic world view ever really challenged. Far from turning him into a cynic, the War has made Chris, if anything, even more of an idealist than before.
At the same time, it's notable that Chris doesn't confront his father about his sharp business practices sooner. It is surely this that Sue has in mind when she accuses him of "phony idealism." In other words, Chris's high-minded ideals seem to fall short when it comes to his own family. In that sense, one could reasonably describe Chris as a realist. But it would be more accurate to say that Chris has been lying to himself all this time, trying to suppress the nagging sensation that perhaps his dad really was guilty all along.
Either way, Chris's direct challenging of his father's actions does seem a little too late in the play for us to regard him as a genuine idealist.