What can I do to protect an elderly person from being exploited by someone who he thinks is his friend?

You can call the non-emergency police number in your town and explain the situation to an officer. The police might already be familiar with these people or they might decide to visit them in a casual way to let them know they're being watched. At the very least they can give you some advice on protecting your dad and his stuff.

I called the police once about a suspicious man who was staying in the motel I was in--it turned out he was dealing meth and they had a warrant for his arrest.

You never know...

To answer the question, I do not think she has a business but she has paired up with someone with an interest in his antiques. I do not know that person very well and do not know much about their connection.

Is this woman an individual or does she own a business? You may be able to report her to the attorney general or the BBB, whatever you can throw at her to intimidate her, As suggested by others, a security camera may work but if your dad is giving her permission to take his stuff, it's not theft unless you can prove his vulnerability. Maybe you can get a restraining order against her? I'd be worried about her doing something worse than taking items, like convincing him to make her his PoA. He can totally do that without your knowledge or consent. There are people who are professional elder predators (my cousin was a victim of this). If you have PoA for your dad, make sure it is a Durable PoA so that it stays in effect even when he becomes mentally incapacitated. Good luck!

Technically, he is still seen as mentally competent so he drives, goes on walks, visits friends, reads, and cooks for himself.

As is sometimes the case, people in this category can be confused about certain issues and they can probably not be judged as mentally incompetent just because they're forgetting names or being irrational about certain topics.
For this reason, I'm not always around the house and have a multitude of obligations.

I think the suggestion about a spy camera is a good one.
He is the sole owner of the house and the antiques are legally his and he usually insists on having whoever he wants at the house even if he knows I don't like them.

I think why he has gotten rid of certain scammers, including the one who stole from me, is just his own preference and also because I was able to prove that he trespassed onto our land as if he owned it and was bothering both of us.
This lady that wants to move his antiques out does know I don't trust her since she's been confronted and what amazes me is her lack of concern. If she knows she didn't take anything, then she might be able to figure out that it was the person with her who stole things with her in the general area and she should take a protective stance. I was wondering if why she had a temper fit when she was confronted is because of her guilt. I think some people steal just to be obnoxious and not because they need what they're taking.

As for antiques not selling anymore, I agree that it would be true in certain areas.
I would also agree that it might be true for certain age groups.
The antique dealer I talked with said their non-salability is only true about certain items. I looked on the web and found hundreds of recently sold items similar to ours.

Who owns these antiques, you, your father or both of you? And, how did you convince your father to get rid of one of these scammers? Would it work again? Dad has dementia? You can always warn her that if Dad does have cognitive issues and she continues her pursuance of his valuables (and it sounds like yours as well) you will notify the authorities and have her prosecuted for taking advantage of an impaired Senior.

Sell one of the antiques you are not that attached to and have a security camera system installed inside and outside the house. Be sure to utilize the “these premises under video surveillance.” stickers Then, when this person “visits”, show her the camera system. Some have sound so you can record anything she says to Dad. You don’t need to be nice or even polite to her. As far as that goes, if you know what she’s like, why are you even letting her in? Are you leaving her alone with Dad? That’s a BIG NOPE! She needs to realize you’re onto her. As far as that goes, you shouldn’t even be letting her in the house. Why are you? If Dad carries on, tell him very honestly that she’s actually stolen from you and continues to try to scam him. Because she knows you have so many valuables in the home, I’d be concerned she will not stop at trying to scam Dad and may enlist the services of lowlife friends who will rob you. I might sell another piece and rent a climate controlled storage facility. Once the pieces are gone, so will she be.

You don't have to allow anyone into your house without you there. Also, you do not say if your father is in his right mind? If he is suffering from dementia you may be correct in being worried. As someone who has bought and sold antiques most of my life I can tell you that values are way down. No one is collecting now. I think there is more collecting still in certain parts of the USA, such as the south, and less in such places as California (unless it is mid-century stuff). My brother and I always giggle about the old "But it is worth blah blah" because the truth is it may be WORTH it, but is it being sold. Businesses even to smaller antique malls are failing right and left. Very few in San Francisco. Just not what the millennials are into. They like to eat out.