From my position, a actual "Hate Campaign" would be an organized attempt to (literally) harass a target with hate mail to the point that they are actually restricted from operating a normal life. It can be very closely related to a "Smear Campaign" which is explicitly defamatory.

So for example, back in the 90's, if something turned into a media circus, it's possible that the target of the reporting could be getting thousands of letters every day, thousands of phone calls every day, and even hourly visitors. Double the level of danger if most of those callers are saying shit like "I'll find you and I'll kill you". If your mail can't be delivered properly, then you can't respond to your normal bills and communications. If people won't stop calling you on the old land lines, it means you can't even make calls out of your home. If people keep coming to your door at literally all hours, you can genuinely be made to feel unsafe.

This did occasionally happen, but it was rarely organized. When it was, it was typically organized by the media. Tonya Harding is one that sticks out to me because she was locked in an apartment complex. The news basically doxed her location and it allowed people to start doing all of the above. The phone didn't stop ringing at all hours until she pulled it out of the wall. The media & papperazi surrounded her complex for days, to the point it filled out the parking lot. They then contacted and harassed the property owner; who decided that she needed to leave, and walked to the room and basically asked her to leave. She didn't feel like it was safe to come out, because of the baying journalist mob that was screaming at her through the doors and windows standing a foot or two behind the apartment manager. Then, one of them came up with the idea to call a tow-truck company and have her car towed away so that they could get pictures of her. They did exactly that, and got pictures of her basically in a disheveled state chasing after her car, while they all took billions of pictures of her, screamed at her, and then ran with the headline that she was attacking journalists because she was clearly insane.

She, obviously, Tonya Harding committed battery, but it kind of shows you the lengths that the media is willing to go. Fundamentally, they wanted pictures of her, and wanted to construct a narrative about her, so they sent out a journalist lynch mob to use any mechanism to get that. Not only that, but when you look into it, you'll see that most lynchings and race riots seem to also be directly tied to media actions. You don't hate journalists enough.