Science is not religion. Science is a methodology by which the natural world can be investigated and understood. Our understanding is imperfect and our information is incomplete, but that methodology by which we reliably expand both works.
I consider myself a (somewhat decreasingly) religious person, and I do believe in God. But I do acknowledge that my belief is based on ... well, emotional and personal experiential evidence rather than anything empirical, so I may be mistaken on metaphysics. If there is something beyond the natural world, then the religious are correct that it would have to make itself known to us via revelation, but there is no revelation that can be considered true a priori. There are multiple competing and often incompatible claims of revelation--and often, mutually incompatible interpretations of them. The only grounds that we possess for deciding which—if any—to accept are reasoning, logic, and observation
Science cannot say which one is the correct one because science deals with testable phenomenon within the natural world. However, when a religious system makes a real-world claim, then science can evaluate that claim. If someone claiming revelation predicates the truth of that revelation on empirical facts known to be wrong, then it is infinitely more likely that it is their claim of revelation and not the real-world observation that is in error. Mohler often refuses to give people a 'theological pass' to abandon young-earth creationism. But Mohler has it backwards: the claims of theology do not trump empirical observation, rather, it is by empirical observation that they are tested. On what grounds does Mohler demand that we accept his claims, if not on the grounds that they are borne out by observation? I'm-right-and-you're-not just doesn't cut the mustard. 'The Bible says' doesn't cut it, either. That merely throws it back a level--on what grounds do we accept the Bible?--and complicates the issue: even if we accept the Bible, then why do we accept Mohler's interpretation?
The reason that Mohler is so insistent that his theology must trump reality is because it fails the reality test. An old Earth would indeed invalidate his theology as he says. However, it does not follow that every observation of such must be wrong. Rather, it follows that his theology is wrong, because the Earth is in fact old.