Is it always non-racist to criticize a religion? Even if we disregard ethnic
Your opening question, I think, is relatively easy to answer: it's not *always* non-racist to criticize a religion. Sometimes it is racist because the criticism is motivated by racist attitudes. You may, for example, loathe race X, and you know that all of them are, say Christian. With that clearly in mind, you criticize Christianity, and this is an expression of your racism towards X. Another example: you are trying to compare religions, to see which ones you think are particularly "bad." You notice that Religion "R" is practiced predominately by white people, and you hate white people. This biases you to criticize R more harshly than other religions, and you conclude that R is the worst religion. This is again a criticism of a religion that is, at least in some sense, racist. So it is possible to launch a racist criticism of religion.
I'm not so sure about your suggestions relating to this question, though. Consider the two most popular religions on earth (I may actually be wrong about this... but at least some years ago these were the demographic facts as I learned them): Christianity and Islam. Christianity is followed by millions of white and millions of Hispanics (not to mention millions of Africans and millions of Asians...). It started out, of course, in the middle east--we count Semitic peoples as "Caucasian" but that's never stopped white racism against Semitic people. Those are different races, and I don't think it's accurate to say that Christianity is dominantly white or dominantly Hispanic, for example. One may associate Christianity with Europe, so one who is racist may criticize Christianity in a racist spirit; but it doesn't follow that *any* criticism of Christianity is racism against Europeans. One may just criticize the doctrines and policies of Christianity, as they are believed and followed throughout the world's peoples. Now consider Islam. Iranians, East and South Asians, and several African ethnicities are not Arab. Here, though you might think that Islam is "predominantly" an Arab religion, I think the suggestion would go wrong exactly when it comes to the issue at hand: critics of Islam often have the beliefs and policies of practitioners from those other ethnicities in mind. An Indian critic of Islam may well have Pakistanis predominantly in mind, not any of the Arab nationalities. And, while we're at it, we should note that the most populous Muslim country (at least as far as I know) is not an Arab country (it's Indonesia). So, this leads me to have doubts about your assumption, that religions generally are associated with a single ethnicity, especially as we consider religions as the target of criticism. Finally, I also have doubts about the suggestion that culture arises from race, but this is an even larger question, about which many, many more facts would need to be brought to bear.
To sum up: for what it's worth, I think clearly some criticisms of religion are motivated by racism. But we shouldn't dismiss *all* criticism of a religion as mere racism. Other philosophers here may disagree with me, so please don't take what I've written as "the philosophers' view." There has been some discussion about particular cases that may be relevant to your interest here. For example, see the Sam Harris controversy concerning his remarks on Islam (though of course you may have had this in mind originally).