1. It's fine for people to change their profile pictures "in support" of a cause. It's also fine for people to not do that.
It's an avatar, so maybe don't get too worked up about it either way. It's a nice gesture and does absolutely no harm to anyone. There are more important things for you to get upset over, so best move on.
2. AVOID COMMENT SECTIONS OF ANY NEWS ARTICLE PERTAINING TO SAID TERRIBLE THING.
Like, this cannot be repeated enough. Just don't go in there. It's not worth it. You're not going to change anyone's minds, it's going to be filled with sincerely horrible things being said AND horrible things being said by trolls to elicit emotional responses, and you're going to leave feeling awful.
Actually, just always avoid comment sections for every article ever. They are literally never good or rewarding in any conceivable way.
3. Be reeeeeeeeeal careful about sharing news stories where individuals are named.
For the story on the poor guy being photoshopped in the image for this part, read here.
It might be important for you to share a news story about the terrible event, which objectively occurred and that cannot be argued. But when it comes to naming individual people, be a lot more careful. Keep in mind no one is FORCING you to share stories, so there's really not a good reason to do so until everything is 100% confirmed (and even then, why are YOU sharing it? What extra commentary could you possibly give, unless you actually know the person named?).
Here's the problem: early reports get shit wrong A LOT, and innocent people are named as attackers and terrorists, despite the total lack of veracity. Take the time an innocent dude was accusing of killing a group of school children. Or the time MULTIPLE innocent people were accused of detonating a bomb at the Boston Marathon. Or when a VICTIM was confused with a TERRORIST in the wake of the Paris attacks. Or this guy, who was identified as a cop killer falsely and has gotten thousands of death threats because of it.
Just, uh, be a little careful in spreading false information, cool? Cool.
4. Don't give people shit for making stupid jokes.
In the wake of a horrible thing, people have weird gut reactions that you may find offensive or disagreeable in some way. And there's a good chance that their reactions ARE offensive or disagreeable! But don't give them shit over it, and don't start an internet slap fight. People react to things poorly, or not enough, or too much - I mean, you've probably had stupid, not thought out reactions to a million things too. Everyone does.
Maybe that thing was that you tried (and failed) to make a funny joke about a terrible recent event - you were thinking you'd bring some levity to an internet dominated by doom and gloom stories about misery and loss - after all, humor is a coping mechanism for traumatic events, a way to minimize the horror of what's happened in our minds. Still, others might find it in bad taste.
But here's the thing - leave it alone. Don't shame them for their shitty jokes. Odds are they'll regret whatever shitty reaction they had in a little bit, and that regret will haunt them for their entire lives. They'll be sitting in bed one day, and their brain will suddenly pull out "HEY REMEMBER THAT TIME YOU MADE A SHITTY TWITTER JOKE ABOUT A TERRORIST ATTACK, YOU FUCKING INCONSIDERATE JACKASS?!"
Nothing you can say will match their own self-loathing.
5. Don't give people shit for caring about this ONE terrible event but not caring enough about ANOTHER terrible event.
Do you know how much horrible shit happens in the world EVERY DAY? SO MUCH TERRIBLE SHIT. If you were able to actually emotionally take in the amount of suffering and misery that people went through, you would be a catatonic ball of grief and terror. You wouldn't be able to function.
The world is full of awful, unspeakable atrocities - so many people are abused, murdered, and hurt every single second of every day, it's unfathomable. And some of these events will make their way into the news cycle and have a profound effect on you - and then another one will come along, and not affect you quite as much. That's fine.
So yeah, some people are going to make a big deal out of ONE terrible event even though they didn't make a big deal out of an EARLIER terrible event. And that's okay! They're expressing empathy, and how much are YOU helping by wasting your time shitting on someone over the internet when you SHOULD be getting back to your work at Doctors Without Borders, which is definitely what you must be doing with your life if you're so high and mighty all of a sudden.
6. Don't give people shit for "slacktivism"
Again, if people want to share things online related to a terrible thing, you can't give them shit for not doing ENOUGH. Would you rather they just not do anything? It's okay that people share an image macro saying "PRAY FOR PARIS" - sure, it doesn't really solve anything, but it doesn't hurt anything either. It's not like you should expect everyone to suddenly do incredibly meaningful actions that will suddenly cause massive changes in the world every time a terrible event occurs - people have their own lives and their own problems, and if they wanna show some empathy on the internet, that's a GOOD THING.
So if people make a dumb joke, or make a big deal out of one terrorist attack but not an earlier terrorist attack, or appear to be making said terrible event too much about them, just leave it be.
Addendum: Giving 'parody accounts' shit for opportunistically changing themselves into some kinda thing specific to the terrible topical thing is COMPLETELY fair game.
7. Just, generally, be nice and not start shit with anyone.
There's a ton of horrible shit in the world. Don't add to that. Don't leave shitty comments on people's Facebook posts because they shared a Minions meme (even though Minions memes are objectively bad). Don't tweet at someone that they're an asshole or have shitty opinions (even if they do). Try to be a force of positivity in the world. Post on someone's Facebook that they're rad as hell, even if they're only rad as heck. Like their Instagram selfie, even though you think selfies are self-indulgent bullshit. Retweet their dumb @midnight joke, even though it's a terrible pun about cereal names for the Hunger Games.
You're not going to solve the problems of the world, but you can at least make one stranger on the internet slightly happier.
Reminder: Don't read the comments of this article.