delericho
Legend
Should I be offering them more moral choices? Or is a campaign that doesn't emphasize good versus evil enough?
Should I be putting the party in more morally ambiguous situations? If so, how do I generate such situations?
It depends on the specifics of your group. I would probably try it once, and see if they bite. If they're interested, do it again; if not, don't.
The classic way to construct a morally ambiguous situation is to present them with a situation where whatever decision they make (including no decision) has both good and bad consequences, so there can be no 'right' choice. Probably the classic is: if you went back in time, should you kill the infant Hitler? On the one hand, murder; on the other, well, we know. But I do advise trying to be a little more subtle than that!

Am I subtly steering them towards 'good' when they get out of line? If so how can I avoid this?
Just... don't. Let them make their choices, and proceed without comment.
Are there settings that are more conducive to morally gray games than others?
Probably, yes. A setting that is itself rather dark is likely more conducive to shades-of-grey - something like Ravenloft, or Dark Sun. Or a somewhat political setting - Eberron can work well.
But shades-of-grey can be done, and done well, in most settings. Though I daresay trying to write a shades-of-grey Superman story might be a challenge.