Marxist-Leninist Liberation Theologians invoke the name of the Christian God to justify bloody Communist revolution and the destruction of the USA. Does the notion that Liberation Theology is not Christian also fall under the “no true Scutsman” falacy?
And yes. If anyone who claims to be Christian and claims salvation in his name, isn't a “true Christian” because you disagree with them (like perhaps Obama and the Rev. Wright) then THAT TOO is a “No true Scotsman” fallacy.
But why the attempted change of subject? Do Liberation Theologists cut the heads off people chanting “God is Great”? No they do not. However Islamists regularly cut peoples heads off chanting about “Allah” being great.
Your position is that anybody who does anything reprehensible couldn't possibly be religious. That is a sterling example of the “no true Scotsman” fallacy.