Some people have these “lives” very separated so that they don’t touch each other as much. But other people have them very blended together (e.g. their RL work, family, and friends are online or accessible via online means). The latter becomes more of a thing as the world continues to rely and depend more on technology and the web. And in any case, even if you cannot directly affect the physical reality of someone, you can still significantly affect their mind and emotions (especially if they’re vulnerable) - which can consequently affect their physical reality. Not to mention, creeps are not as unlikely as one would like to believe and may creep as far as threatening your sense of safety for yourself and your loved ones (and yes, even invading your privacy). So while there’s still some distance, there’s still power that can be used and abused.
If you’ve experienced abuse right in your close surroundings, that is very likely worse if the person(s) exerting the abuse is just as cruel as someone who’d choose to torment someone via online means. However, it’d still be oversimplistic to dismiss “Online” experiences as not real enough simply because they happened online. Harassment is harassment regardless of where it takes place. If someone is being clearly and severely harmed by your actions and you continue to perform them, you do not get to claim you did no wrong because it happened while you were online and be correct about that.
This is a complex subject in which there are many rules and exceptions to all of them. Nevertheless, it helps to try to distinguish between when one is only having their ego offended and when one is suffering from crippling damage caused by malicious or disregarding individuals.
See also: What is abuse?