It doesn't, since provided it is supported by an appropriate methodology you are perfectly free to present evidence that is mutually exclusive from naturalism - over to you.
That's been done, several times, over the years, Gordon - but it has simply been dismissed as being non-naturalistic in nature and therefore irrelevant
So you have, but you've failed to demonstrate the latter.
Sorry, Gordon, but I haven't failed to demonstrate anything; rather, the non-naturalistic aspects I've referred to have generally been ignored or explained away in an un-naturalistic manner.
However - let's take reality. What is it?