Ed M. answered 12/13/15
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I agree with Bruce Y. about none being ungrammatical in your sentence for the reason he gives, but I'd like to point out that no one could also be appropriate in this context, i.e., Some religions have no one deity . . . . So perhaps the source of the "error" in this sentence is a confusion between none and no one--or possibly even a typing mistake--which actually reflects the historical relation between these in that none ultimately derives from Old English ne an 'no/not one'.
But I must say that I think the second correlated and reduced clause in your example, are philosophies that function instead of religions, presents a couple of problems, if not strictly speaking "grammatical" ones. For one thing, your whole sentence is a bit of a tautology, that is, a sentence that doesn't say much or is even meaningless because parts of it just repeat each other. In this case, the grammatical subject of the entire sentence is some religions, which you describe in the correlated clause as being philosophies that function instead of religions. In other words, how can a religion also be a philosophy that "functions instead of" a religion?
Also, the verb functions itself may not be semantically appropriate. I think I understand what the entire sentence is trying to say, i.e., some religions are more like philosophical systems because they don't have any "gods," but the verb function implies a much more utilitarian, practical use for something that we usually don't ascribe to a people's philosophy or belief system. For example, you could say something like The king functions as the head of government because, in our understanding, every government requires a "head" or a symbolic or actual figure of authority, but no society "requires" an "official" religion or even philosophy (unless this is a principle of some sociological theory I'm not familiar with). I'm just thinking a verb like serves might make more sense here.
But I must say that I think the second correlated and reduced clause in your example, are philosophies that function instead of religions, presents a couple of problems, if not strictly speaking "grammatical" ones. For one thing, your whole sentence is a bit of a tautology, that is, a sentence that doesn't say much or is even meaningless because parts of it just repeat each other. In this case, the grammatical subject of the entire sentence is some religions, which you describe in the correlated clause as being philosophies that function instead of religions. In other words, how can a religion also be a philosophy that "functions instead of" a religion?
Also, the verb functions itself may not be semantically appropriate. I think I understand what the entire sentence is trying to say, i.e., some religions are more like philosophical systems because they don't have any "gods," but the verb function implies a much more utilitarian, practical use for something that we usually don't ascribe to a people's philosophy or belief system. For example, you could say something like The king functions as the head of government because, in our understanding, every government requires a "head" or a symbolic or actual figure of authority, but no society "requires" an "official" religion or even philosophy (unless this is a principle of some sociological theory I'm not familiar with). I'm just thinking a verb like serves might make more sense here.