I find it funny, this need to collect and group people.
Ultimately, everyone agrees there are 'the bad guys' and everyone wants them to lose. The bad guys are Muslims, so some people (like example person 'Alex') turn around and say 'Muslims are the bad guys'. Alex then decides he has a strong dislike for Muslims.
But clearly, not all Muslims are bad guys. Alex gets around this problem by stating that these 'self-described Muslims' are not really true Muslims. Because Alex knows that all Muslims must be bad guys.
In other words, Alex is an idiot and the irony that he is vocally discriminating against a group of people, in a way that is not too dissimilar from how the actual bad guys blindly hate the rest of us, sails over his head - weeeeeeeeeeeeee!
It's a shame people get bogged down by this nonsense rather than tackling the issue that really matters - finding, stopping and beating the bad guys. That is not to say that characteristics of terrorists, such as their faith, are merely coincidental. The fact is that the biggest terrorist threat we face today comes from a Muslim group. Bad guys they remain, nevertheless, and that is what truly matters.