There are already at least a couple of questions (1, 2) about how to handle potentially inappropriate profile pictures, but the answer given in both cases (and other duplicates of those) essentially comes down to "flag it and let the moderators deal with it." Well, as a moderator, how exactly am I supposed to deal with it?
As far as I can tell, Stack Exchange does not have a clear policy about what sorts of images are inappropriate. The closest thing is this clause in the terms of service:
Subscriber represents, warrants and agrees that it will not contribute any Subscriber Content that [...] (d) is libelous, defamatory, abusive, threatening, harassing, hateful, offensive or otherwise violates any law or right of any third party....
but people do not always agree on what constitutes hateful or offensive content, or even on what constitutes libel or defamation (considering the prevalence of lawsuits). I don't think it's reasonable that my own opinions on the topic should be the basis for judging whether a picture is acceptable or not, simply because I'm the one tasked with handling (or not handling) the flag.
I'd like to establish a more specific policy to guide moderators tasked with handling potentially inappropriate profile pictures. Certainly I'm not suggesting we set up an exhaustive list of inappropriate profile pictures, but something more than what is in the ToS would be useful. For example: "X, Y, and Z are always inappropriate; for anything else, defer to the community team," with specific details about what X, Y, and Z are. I have my own ideas, but I'll omit them to avoid influencing the responses.