How do I deal with it was your question. Personally, I've never felt ignoring a borrower was the smart play.
First of all, you need permission from the client to discuss the appraisal with the borrower. If I can "convert" the borrower I will try. Conversion means listening to their concerns, explaining why data they provided is not relevant if that is the case, and/or demonstrating a willingness to make a change if one is warranted. I'm not going to be pushed but I will listen.
I don't have many problems these days with borrowers as there is usually sufficient market data in the form of current listings to convince borrowers what their properties are not worth.
In your case I would simply explain that whatever is going on in the subject market it should already be reflected in the sale prices of comparable homes. Anticipation about future events is already reflected in the prices knowledgable buyers and sellers agree upon.
Sure, you can just tell the borrower to take a hike if you do it politely. I'm not sure if that is a win-win approach. The way I see it if I can "convert" the borrower I've protected that client's relationship with the borrower and my own reputation as well.
Make a friend if you can. It is just plain stupid to cut yourself off from the borrower public. Who knows if that borrower will be in the position to recommend you to do an appraisal for an estate, or a divorce or a tax appeal? Right now that borrower might want what he wants. Tomorrow he might want an honest appraisal completed by someone who is going to tell it like it is, like when their spouse is trying to screw them or their siblings are fighting over the estate.