In discussing the response to Nidal Malik Hasan, Alonzo Fyfe draws the distinctions just right when he accuses atheists who leap from the act of one kind of theist to associate theism in general with violence as an instance of “The Bigot’s Fallacy”:
Many of the people who embrace the Bigot’s Fallacy in this case are quick to argue that nobody has ever done any harm in the name of atheism. The argument (the version that makes the most sense) begins with the premise that atheism is a belief that the proposition that “at least one God exists” is certainly or almost certainly false. This belief alone doesn’t tell anybody to go establish a dictatorship and slaughter millions of fellow citizens. Therefore, it makes no sense to blame these atrocities on atheism.
The anti-religious bigot simply ignores the fact that the same argument applies to theists. The parallel argument begins with the premise that a theist is one who believes that the proposition that “at least one God exists” is certainly or almost certainly true. This belief alone doesn’t tell anybody go fly airplanes into civilian sky scrapers or to murder people in a processing center at an army base. Therefore, it makes no sense to blame these atrocities on theism.
The problem, in the latter case, is a set of specific beliefs that one attaches to the belief that at least one God certainly or almost certainly exists. It has to do with beliefs about what that God wants. However, there are also belief sets that include the proposition that no God exists that are just as capable of motivating a person to establish dictatorships and promote mass murder. So, still, the two arguments are parallel.
Among the various atheist philosophies there are a few that put a premium on reason and evidence. Among members of that subgroup of atheists, there should be some way to introduce a moral objection to the Bigot’s Fallacy and similar breeches of reason. These options are to be shunned – not because it is politically useful to be nice to theists, but because good people condemn the use of fallacious inferences in themselves and others.
Having said this, the Texas shooting does provide good reason, not to go after ‘theism’, but to go after any specific religious teachings that seemed to support the shooting, and any person who speaks for a specific religion who praises the shooting.