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Like Conan said, I think it may depend on what you're swapping coconut milk for cream in. I'm not as sure about how just plain cream breaks down chemically, but milk itself behaves like a buffer solution- when my problems with heartburn were much worse, milk was one of the few things I could eat or drink that would take the edge off a bad day.
So it might not be that coconut milk causes heartburn as that it's not as good at buffering extremes from other sources as what you're replacing.