I remember a video about how Tolkien intended Smeagol/Gollum to be allegorical to someone who fell innocently into an addictive sin as a non-Christian, then was forced to become friends with a pair of Christians and tried to set himself straight, but ultimately failed and the sin led to his downfall. It makes sense, but can anybody verify this?
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I haven't heard that theory. However, keep in mind that Smeagol committed murder in order to get the ring, so he didn't innocently fall into sin. Murder is a sin in other religions as well.
Besides, Tolkien didn't like allegory, so he probably wouldn't have thought of Smeagol's story that way. It's possible, but unlikely.
Still, it's an interesting theory and worth discussing.
The act of murder was technically committed as a result of the sin, in this case to engage in it.
It seems unlikely that Tolkien intended such an interpretation as he famously hated allegory. But a reader brings their own experience to a book with them--often to the surprise of the author.