IANAL, but I think your #1 and #2 do apply most of the time for anything that can be seen in the public. Defamation of people's religions in a dis-respectful way is generally unlawful (though maybe not illegal). The act of giving someone the finger is generally regarded as a sign of violence.
You might have more liberal views than me, but I do think it's a violent gesture. I get the point you're trying to make, but I simply disagree that for this specific case, this should be something that is generally acceptable in a public social network with 13+ year olds on it.
"Defamation of people's religions" falls squarely under free speech in any country that has it. And if you consider "defamation of religion" a "violent gesture", consider re-examining your values. The attitudes you suggest would fit right in in countries still ruled by religious bodies, but they have no place in in civilized societies. (Any country that still places restrictions on speech, or intertwines religion and government, hasn't quite figured out "civilized" yet.)
Also, "unlawful" and "illegal" mean the same thing.
Now, I'd absolutely agree that defamation of religion can potentially offend people. And I suspect that if someone had a profile picture that defamed someone's religion, Google would remove that one too, because they want to keep profile pictures inoffensive to most of their target audience. That does not make such images illegal, though.
For that matter, promotion of religion can potentially offend people, but I doubt Google would remove profile pictures with overtly religious messages, because they don't particularly care about the small number of people offended, and they don't want the massive backlash from religious people, whose ability to stir up angry mobs has only grown with modern technology. (Oops, I've defamed religion there.)
Google could also choose to delete all profile pictures that contained the color red because they don't fit a preferred color scheme. If they did so, they'd attract quite a lot of complaints and ridicule, but they certainly have the right to do it.
- if anything were said / written criticizing the Bible, then a single devout Christian could deem it offensive and it would be removed?
- if a woman's picture without a burkha were posted, then a single fundamentalist Muslim could declare it offensive and it would be deleted?
- if a "blonde" joke were posted, then a single radical feminist could call it offensive and it would be eliminated?
Doesn't sound like an online world that I'd want to participate in.