One of the core ideas of 'if' involves uncertainty. see: http://www.gramorak.com/Articles/If.pdf
With some verbs expressing in themselves lack of certainty it appears that THAT and IF can both be used, with little practical difference in meaning between:
1. I doubt if he could do the job.
2. I doubt that he could do the job
In  the uncertainty about his ability to do the job there may be stronger than in ; only the context of the utterance can make this clear. The difference is not important for practical purposes.
With absence of doubt we return to certainty, and THAT is now the only appropriate choice:
3. I don't doubt that he could do the job
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