Fatwa envy

Fatwa envy is the term used for the phenomenon of people complaining that criticism of their religious or political beliefs is hypocritical, on the grounds that similar criticism would never be directed at Muslims for fear of violent reprisals (or, in a related argument, because of political correctness). This complaint is widely associated with Poe-like Christians, although more secular wingnuts have also been known to use this argument.

Nature of the condition
The rants of Fatwa-envy-filled posters generally start angry, upset, or frothing at what the target said or did. The screed then turns to how the other religion would not tolerate what was said (almost as if the person ranting wishes they or fellow religious brethren would turn to violence or killing). To complete the rant, the ranter usually prays for or forgives the target, or explains that they will be going to hell if they do not repent for alleged sins.

Fatwa envy is full of lulz because the ranter does not understand that a loving and forgiving religious person would not imply that they'd like to see violence done to those who disagree with them (at least not without openly criticizing themselves for it), and would (at least try their best to) forgive any supposed wrongs before making veiled half-threats on a blog or forum.

Plenty of "New Atheists" have indeed criticized Islam just as strongly as Christianity and Judaism, and have legitimate concern for their lives as a result. Additionally, criticism and "blaspheming" of most mainstream religions can and does result in death threats — see the PZ link below for an example with Catholicism. It could be argued that the Enlightenment alone is all that made Christian Europe into something noticeably more "tolerant" than the Islamic world; within the whole of Christian history, it's astonishingly recent for heresy and blasphemy to not be capital crimes.

Fatwa envy could be compared to Holocaust envy. However, while fatwa envy expresses a desire to use force, Holocaust envy expresses a desire to receive compassion.

If you strip this argument to its core, it is nothing more than a not as bad as fallacy (atheists are ungrateful bastards for criticizing the actions of a particular religion whose followers aren't slaughtering them on a whim) coupled with tu quoque (atheists' critiques are invalidated if they're deemed hypocritical or inconsistent in applying them) as well as a non sequitur (not criticizing a certain group, whether it is because they are righteous or dangerous, has nothing to do with the validity of criticism aimed towards a different group).

Meaning of Fatwa
In actual real-life Islam, a fatwā is any official religious opinion regarding Islamic Sharia law issued by a Muslim scholar, somewhat equivalent to a Vatican proclamation, but usually with much less "official" authority (as Islam has no central leadership, thus anyone who has studied the Quran and hadith enough can become a "scholar" — Osama bin Laden included).

Following the Salman Rushdie affair, however (in which the author of The Satanic Verses was condemned to death in a fatwā by Iranian leader Ayatollah Khomeini — who had more authority than most, being one of the most revered figures of Twelver Shia Islam), the term has, in many Western minds, become synonymous with an Islamic death sentence, though that is in fact a rare use of them. Now you know (and knowing is half the battle).

The fatwa envy jamboree
Some nice examples of atheists criticizing Islam, despite, according to their critics, not having the stomach to criticize Islam. Warning: exposure to this may induce cognitive dissonance.

Richard Dawkins

 * Dawkins: Islam is 'one of the great evils in the world'
 * YouTube: Richard Dawkins destroys Muslim on morality

Johann Hari

 * "Sharia courts highlight in their purest form the problem with multiculturalism."

Christopher Hitchens

 * YouTube: Christopher Hitchens on Islam

Bill Maher

 * YouTube: Bill Maher asks: Is Islam a religion of peace?

Maryam Namazie

 * "Political Islam is the problem"

Examples

 * former Archbishop of Canterbury Lord Carey: "I doubt that Bowie would have the courage to use Islamic imagery - I very much doubt it."
 * Conservapedia's Comedy Central article, discussing the network's alleged hypocrisy because it did not show an episode of South Park which featured a depiction of Muhammad, even though the show often satirizes other religions.
 * PZ Myers' special "Cracker" edition of "I Get Email" on his blog Pharyngula.
 * Dan Piraro's 2013 christmas Bizarro netted him a beautiful example, lovingly shared by "an American Christian": "Would you be equally quick to offend Muslims with a cartoon strip eluding to a recently departed Muslim complaining of only receiving 35 vestal virgins or showing one of someone asking a blind person if they’d seen any good movies lately? For less, Salmon [sic] Rushdie received a fatwah for writing Satanic Verses." That's the spirit of the season.