It depends somewhat on the particular moral grey area you are worried about, but in general I don't think your characters don't need to be moral in any particular way, but IMO when your target audience are young and/or impressionable, you should take at least a little care in presenting the story, or at least the immoral/amoral aspects, in some form of moral perspective, or at least draw attention to the moral question at some point. The main thing to avoid is portraying the questionable aspect as common or acceptable or what have you. If your MC is a thief, don't let him get thought the whole thing without somebody (himself or another character) questioning its moral implications, or else facing its consequences. If your characters are vikings, its entirely possible that they will spend much of their time raping and pillaging, and may not ever think bad of it, but somewhere you might remind the reader that the lady might not appreciate it. This is one of the complaints I hear most often regarding a certain shiny vampire series: that an angsty, obsessive, possessive, and often violent relationship is common and proper and something to strive for. Not that any of that is all that unusual in a vampire setting, but it never really pointed that difference out, and as a result a whole crop of pre-teens are going to have dreams of a kind of relationship that in the real world just causes damage.
</soapbox>
This is one of the few instances IMO that is easier to handle in a 3rd person POV than a 1st. In 3rdPOV you just have to slant the narrative tone slightly, and you can usually keep everything grounded enough. But in a 1stPOV, your narrative voice and tone cannot so easily diverge from what your character themselves is supposed to think/feel about the matter (unless you are narrating in a future musing memoir flashback sort of a way, which lets old MC comment on the foolishness of his own youth or whatnot). In those situations, it usually takes another character or event within the story to draw attention to the particular morality you are trying to preserve, even if its simply by contrast. Or there is the redemption path, but then the morality is a central theme to the story, and is in no danger of getting lost.