Persecution of Christians in the Middle East
(I should note, though, that as long as cranks like Tom Cotton tell gays in the US not to complain because gays in the Middle East have it worse, the same point could be made about fundies who claim they're being persecuted in the US because of anti-discrimination laws. Being unable to refuse a gay customer hardly compares with being beheaded.)
This narrative, however, distorts reality in two important ways. First, ISIS is not singling out Christians for persecution so much as it is targeting everyone who doesn't fit its hard-line, puritan form of Islam. The Yezidis, a non-Muslim religious minority widely (though mistakenly) considered Satan-worshipers, have actually suffered the most; ISIS has killed many of them by horrific methods such as burying alive, and turned Yezidi women into sex slaves. Shiites, adherents of the "wrong" kind of Islam, have been targeted by ISIS from the start. Women have been killed for the crime of having an education. Gays are simply murdered whenever discovered. Even the destruction of churches in Iraq and Syria fits into a broader pattern of obliterating everything non-Islamic from the region's cultural memory, including its numerous sites dating from pagan times.
Second, and more importantly, the narrative implies that Muslims as a whole are complicit in these persecutions, which is not the case. ISIS is widely loathed in the Middle East and is the target of a sustained campaign by Iraq, Iran, the Kurds, Jordan, and other regional forces to eradicate it. After the beheading of the Egyptian Christians in Libya, Egypt launched a bombing campaign against ISIS targets in Egypt; the state's determination to avenge its murdered citizens was not mitigated by the fact that those citizens were not Muslim. Normal people feel disgust at ISIS's actions.
Of course even before ISIS arose, Islamist extremists sometimes targeted religious minorities including Christians -- but others took strong stands against such attacks, even if their actions were scandalously under-reported in the West.
Of course, actual Islamic doctrine provides plenty of support for what ISIS does, just as the actual words of the Bible make Fred Phelps look like a flaming liberal. But remember that humans are complex creatures and in most cases a person is not defined by the evil of the religion he adheres to. Just as most Christians don't actually support Biblical mandates for killing of gays, slavery, stoning to death for trivial offenses, etc. (and many are only vaguely aware that those things are even in the Bible), most Muslims are horrified to see what hard-line Islamic dogmas look like when ISIS puts them into real-world action, however much they might claim to believe those dogmas in the abstract.
What we actually see in the Middle East is a small, militant, ultra-hard-line minority of religious fanatics unable to tolerate anything different from themselves -- other religions, gays, independent women, members of their own religion who believe somewhat differently than they do, evidence of the greatness of pre-Abrahamic civilization, anything.
Sounds sort of familiar, come to think of it.