Should I allow them to grind down my good teeth when making adjustments to my permanent crown?

Hello sometimes when we do a Crown have to adjust your antagonist tooth. That adjust won’t affect your tooth because is just in the enamel. 

It is not unusual to have to adjust teeth that are biting onto a crown to make sure you are biting in the best way possible. A broken tooth that needs a crown may have broken because the teeth hitting it were causing trauma to that tooth. If you don't adjust the opposing tooth causing the trauma, it will wear down the crown faster than necessary. 
I know you don't want a dentist to adjust a tooth that seems perfectly good to you, but the adjustment is usually a tenth of a millimeter, which is not enough to harm your tooth. Sometimes the good tooth has a really sharp cusp tip and barely polishing it to a rounder shape can help the crown last longer. 
There are a myriad of reasons that adjusting your good tooth would be beneficial. I hope that these examples help.

In a majority of cases the recommended action would be to adjust the crown instead. But there are definitely situations where adjusting the opposing natural teeth makes more sense. Most molars have 2+mm of enamel, making a small adjustment of a tenth of a millimeter or so doesn't hurt anything.