"God told us to" isn't logic unless God is first proven.

Not really. This, for example, is a perfectly logical argument:

  All burritos are Platonists.
  Batman is a burrito.
  Therefore, Batman is a Platonist.

It does not require either of the premises to be proven (or even true, or even semantically meaningful) to be rational.

To be reasonable, on the other hand, is a much fuzzier concept.

You're invoking Sagan's dragon. The burden of proof is on you, not on reality. Until you prove it right, you are wrong and have no argument to make.

"Burden of proof" has no real connection to rationality as such (beyond determining whether the logic itself is valid). It is fundamental to the scientific method, but that's another thing altogether.