[ETA] To clarify, I'm not arguing that all members who subscribe to the same faith generally have a share in the responsibility for an act done for that faith (though there are specific instances where I would), but that you can't secularize a person's actions just because others in their religion disagree. Each individual has a right to determine what their faith entails, and no one but that individual can tell them differently.
Erm, no. That can't be right, because then you can simply say that
literally anything is an X-religion practice simply because some self-described adherent somewhere claims that it is. That leaves no way to differentiate between acts that are actual tenets of a particular religion, and acts which are cultural or personal, or which are the result of mental illness.
Murdering abortion doctors is not a Christian act, because it directly violates the tenets of Christianity as laid out in the accepted body of scripture, taken in context. It's no different from someone claiming to be a doctor, regardless of medical training or lack thereof, and going around cutting bits off of people to save them from cancer.
To claim it's a Christian act requires a tortured attempt at justification enabled by cherry-picking pieces out of context, redefining them to fit said justification. And often the proponents of such murder do not have even that, only bald assertions, or "personal revelation", without any real attempt at scriptural justification. Just as claiming FGM is an Islamic act requires similar cherry-picking and unsupported assertions. There are certainly many different "flavours" of Christianity, Islam, Buddhism, etc. depending on which aspects or interpretations of scripture are most emphasized; but there are always core tenets that unite all the disparate groups. Violation of those tenets must necessarily mean that the violator is outside that group, and not a true member of said group. (Remember, No True Scotsman is only a fallacy if the basis for judgement is not a defining criteria of belonging to the group.)
That is exactly the conflation that the APlussers are guilty of, conflating both positive or negative acts of individuals with the tenets or characteristic of a larger group and claiming that group is inherently good or bad because X. That there is an "X culture" that all right-minded people should be vehemently opposing, despite the complete lack of any evidence of a prevailing culture.
It's important when making any associations to differentiate between variations based on interpretation, and direct violation of criteria defining the group. Claiming a "rape culture" because some individuals of said culture commit rape is a fallacy, as there is no indication that the inherent characteristics of the group, in this case mainstream Anglo-American culture, condone rape, let alone create a "culture" of rape, and quite a bit of evidence to the contrary. But if you cherry pick comments and actions of a few aberrant individuals, and take the vagaries of difficult rape cases out of context, you can build a specious justification for claiming that such a rape culture exists despite an overwhelming cultural antipathy towards rape and rapists.