Does it have to be based on race/color/creed/gender/disability to be harassment?

What is the name of your state? Florida

This pertains to my wife and her workplace. A few months ago her previous supervisor went to a different position in the company and was replaced by a new one. This new supervisor has done whatever she can to make my wife's life miserable pretty much from day one. As far as she knows she has done nothing to this woman to get on her bad side. My question is this: can an employer get in trouble for harassment if they're doing it just because they don't like someone?

It is possible that this treatment could be racially motivated. Of course, the supe would never come out and say "I'm writing you up because I don't like your skin color," so I think it would be hard to prove that race was the motivating factor. It seems to me that if one person is being singled out and having disciplinary action taken against them when all of their peers are doing things the same exact way, then something fishy is going on. Whether or not any laws are being broken, I don't know. That's exactly why I'm posting here.

To answer the question in your subject heading, yes, it has to be based on a protected characteristic to be considered illegal harassment.

My question is this: can an employer get in trouble for harassment if they're doing it just because they don't like someone?

With the law, no. With upper management, possibly, if upper management chooses to do so.

So then her options are
A) Talk to someone in HR or a higher manager to see if she can put a stop to the undesirable treatment
or
B) Get another job.

Does that about sum it up?

Just for argument's sake, lets say this supervisor has a problem with my wife because of her race. What would my wife be able to gather as evidence of this? Would statements from coworkers saying that they have witnessed the supervisor treating members of Race A one way and members of Race B another way be of any help?

Does that about sum it up?

Yes, that about sums it up.

Before we get into specifics, suppose you tell me WHY you think race is involved.