Whenever Christians or Muslims try to separate themselves from other Christians or Muslims, they are committing a fallacy. It's called the "No True Scotsman" fallacy. It sounds like this; "Most Muslims think of Islamic terrorists the same way Christians think of the Westboro Baptist Church."
Want to know how to beat this? Okay. Just say: "So what? That doesn't mean they aren't Muslims, or Christians. You don't get to decide who is and who isn't a part of your faith." That's honestly all it takes. This is a lazy and stupid argument.
It's an argument that might sound like it makes sense, if the person making it tries to justify it, but at the end of the day if someone says they believe in God, or in Allah, or in any deity, odds are they do. We as people don't get to decide some is, or isn't a "true member of their faith". It's a cop-out people use whenever they don't want someone else to be seen as "like them".
We need to be logical and level-headed. We need to be smart. We need to understand that "extremists" make up a very small percentage of Muslims. But that they are Muslims. Despite what other Muslims might say about them.
But there are other problems. Like why the hell is no one talking about the repression of irreligious people in the Middle East? Why are so few Muslims, in Muslims nations, vocally against blasphemy laws? There are real problems, in Muslim societies that will matter more than extremists, in the long-run. Corruption, repression, and the constant threat of death looms in some parts of the Middle East, and one day that'll have to be overcome. Let's work on getting people to examine the entirety of this situation, of why thousands are fleeing.
Don't let people try and say that the extremists aren't Muslim. Because they are. But at the same time, remind yourself and others that there's more to this than mere terrorism. There are bigger issues that will eventually demand solutions. We can't forget that.