No non-christians share the same beliefs as the LotR mythology, so the fact that LotR mythology is different to christian mythology doesn't make it odd that they believe it.
I think christians are attracted to it because it is 'similar' to their religion - LotR has one, all-powerful and all-good God. Also Gandalf has been interpreted as a 'christ' figure by some people. Plus Tolkein was a Christian and LotR espouses many 'good christian virtues' such as loyalty, fealty, friendship, faith (Gandalf has immense faith that Frodo will succeed even against impossible odds) etc.
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For forty days and forty nights
They rode through red blood to the knee
And they saw neither sun nor moon
But heard the roaring of the sea
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