To undermine the extremists means to eradicate the causes that feeds them
Let's be clear on this. The "cause" that feeds them, is the existence of Israel and Infidels in their world. Unless you want to eliminate Israel and convert to Sharia law, there isn't anything you can do to eradicate the cause that feeds them. You can chase your tail, you can try to appease them by giving them the things they claim they want, and they will most certainly accept them, then they will continue to pursue the cause that feeds them, your total and complete destruction.
Winston Churchill described this as feeding the alligator, and hoping he will eat you last.