I used to respond with anger, to tell them to **** off right back, or something like that, insult their masculinity, or challenge them to fight me. But now I think it's better to respond with sarcasm. I didn't get it for a long time, because I believed in saying what you really feel and being direct instead of beating around the bush and playing fake-nice, like this person is being an ******* to me, why do I owe them niceness? And also because I'm not naturally a sarcastic/ironic person, I'm honest and sincere instead, it's how I naturally perceive and process things. And I'm not good at quick thinking, which is another part of that. But now I think I see why this works better. Everyone has faults, just size them up quickly and throw their faults back at them. One thing I've been trying to realize is that anger doesn't necessarily make you tougher or more of a man. And even if you swear at someone, the person who you insulted could still feel like they "won", because even though you got mad and talked back to them, they still got you to lose control of your emotions. If you respond with sarcasm, you still stood up for yourself, but you did so in a way that denied them the satisfaction of making them feel that they touched a nerve.
In the offline world it would be harder, I would have to remind myself to be more mature, be the bigger person.
I do think you should respond some way though, because I think you'll feel bad later if you said nothing. It will feel like you just took the insult/disrespect. I know that's how I felt in the past when I didn't say or do anything back to people that disrespected me. I felt walked all over, and I hated it, but I didn't think there was anything I could do because I didn't think I had power and I didn't want to get in trouble. But eventually I said no more, I wouldn't allow it to happen again. I would stand up for myself always. But, it's actually stronger to remain in control of your emotions, and to deny them the reaction they want - especially people on the Internet, cause they're just looking for a reaction. And when you think about it, that's pretty immature, so it's best to just let them be the immature person instead of letting yourself sink to their level.
Once someone starts to push you around physically though, that's different.