To test the "roof leak" idea, simply close the lid and come back later to see if it's still turning color. Better yet, place a catch pan on the closed lid and see if it has anything dripping into it. Not a likely situation I'd say. POUR some water into the toilet bowl using a cup, from a known water source OUTSIDE of the trailers water system. If it sill turns color your problem has to be something about the toilet. If it does not, then it's something about the plumbing TO the toilet. Do another check using water from another faucet in the trailer, poured into the toilet and if it doesn't change color then the problem is specific to the plumbing to the toilet only or the toilet itself. It's possible that some sealant or gasket material could be leaching out into the water but not sure how that could happen. Since it's a new trailer, once you're done the testing, if you still have no solutions, return it to the dealer and request help locating the problem.
Good luck / Skip