Superman:

He will tell you it's all not true. When you argue he just asks, "Will you believe strangers or your partner?". If you don't answer right away he is a bit hurt but also knows this isn't just a light issue but something more so he suggests you talk to a specialist about this as no one should take a stranger's words that to heart. If you answer him he's very happy and gives you a kiss, assuring the internet just likes to talk about things they have no knowledge on.

Batman:

He just shuts down your phone, computer, etc... When you give him unamused eyes he just answers he will turn it back on if you stop looking at those things. So once you promise to stay away from the negative stuff he turns it back on. You noticed he has disabled all the negative sites so can't look it up that easily anymore.

Wonder Woman:

She notices by how you start to change yourself to how they want, so that's when she will step in and argue with you. Sometimes an argument has to happen for good to happen. Moments like these being so as she has to be sure you keep it in your head you are doing brilliant how you are so stop trying to change yourself to how some strangers want who have no clue about you personally.

J'onn J'onzz:

When he noticed you focusing too much on the negative stuff he tried to talk you into not looking at such stuff but he knows he can't control such things. He saw an idea online so now when you go to the bathroom the mirror's edges are always full of positive comments he printed out of people loving you/your work and some notes he wrote himself of how wonderful you are.

Flash:

He notices by how your face becomes when you read it all, so he's quick to run to you then cover your face with kisses so you are forced to shut your eyes and ask what he's doing. When you aren't looking he tosses the phone on a soft surface and claims he's making sure you don't start believing those untrue things.

Hawkgirl:

She will snatch it away each time, scolding you to stop looking at that while she searches something up. Then she shows it. It are sites full of positive things to say about you so she has to remind you the negative might seem big but the positive is bigger so focus on that instead.

Green Lantern:

He finds it so silly to take what someone on the inernet says to heart. So he will cover it with his hand, firmly telling you to stop it then tries to distract you by asking if you want to go do something or makes you join him in a task.