Every atheist has heard this cry at least a million times, not only is it fallacious, it demonstrates the selfishness, egocentric, and arrogance of religion in one simple phrase. "Stop picking on my religion," or some other variant.
By nature of being an atheist we are inherently dismissing everyone's god claims, usually for lack of evidence (still waiting for just one of you god nuts to present empirical evidence of your claims). Atheist means we are without any belief in any form of god, by any name or description.
Being an atheist does not demand one be a skeptic or even sane, we have our own nuts like those denying medical science and those who think Bigfoot exists. However we all wind up being atheists, eventually, if we use our brains and ask questions.
So what about us vocal or "militant" atheists makes one think that we're picking on their religion and not others? Egocentrism, specifically. Egocentrism is the idea that only you exist, or only your "kind."
Each religion demands that all other religions are wrong, and evil. Thus when facing something like the atheist, with no inherent religious affiliation, it is incapable of demonizing us, or pretending we don't exist, the way it does other competing brands.
Then they feel the need to be the victim, a clear display of selfishness. This is a tactic used by preachers to keep their followers blind, they convince them that everything is out to hurt them just for being them, they are told that being the victim is inevitable and the followers are too stupid to see beyond what they are told by their leaders.
Now the final phase is the one where they believe they are inherently correct, that they have exclusive knowledge which everyone else is lacking. This is the display of arrogance that religion fuels in the minds of the blind followers, they cannot possibly be wrong because they are special and chosen by some magical sky fairy.
Thus they always fall into the belief that us vocal atheists are picking on them, they believe this because the preachers have told them thus as a tactic for protecting the mental engineering done to the believers. It keeps them insane and ignorant so the preacher can continue to profit off their stupidity.
Pity those poor fools, but more importantly, make them show it in public more and more. This is our only tool for fighting this delusion at this time, one day we will have the weight to use medicine to help these poor people.