While I don't think it changes the order of the fields, I can think of three versions of "how controversial is X" that might yield different answers: a person from field X might trust all its results and say it is uncontroversial; a person from field Y might say it is uncontroversially false; clearly there is controversy if we put the two people in a room.

Even at the extreme, physicists make lots of claims about mathematics that the mathematicians reject. Sometimes the claims are precise enough that the mathematicians accept them as conjectures (and aren't bothered that the physicists use the word "proof"), but often the mathematicians cannot even tell what the conjecture means and reject the label "mathematics." I gave some examples here.