If you're 17 can you choose not to talk to the parent who has full custody of you and move in with your other parent?

That is a tough question.  While a 17 year old has the right to or a voice in deciding who has custody, if one person already has custody per a court order, then a modification of that order may be needed.  This is not a yes or no question obviously.

First of all the court would have of modify the existing custody agreement. 

A minor child cannot choose which parent they want to live with.  The court will look to many factors - home environment, income and education of the parents, the child's relationship with each parent, reason for wanting the change, etc. 

However, while a child cannot outright choose where they want to live, if they over the age of 12, a child's preference is given consideration and is one of the factors that the court considers (the older the child, the more weight it is given).