Dig a little deeper and you will see there is little distinction between reason and the heart. Reason begets “rationalization” which can lead to virtually any behavior, moral or not.
I'll agree that "because this is the way we've always done it" is not valid reasoning in itself. But that doesn't invalidate the precedent either. Are we saying today that the morality of all previous human history was defective because they did not support same-sex marriage? Such a stance requires a very elevated sense of one's self morality.
Nothing has changed regarding the morality of encouraging couples to get married and remain faithful for life. No one is tossing that out. All that has changed is the understanding that gay people are not 'defective' or dangerous and should be treated the same as everyone else. Most people thought this for hundreds of years. They were wrong. It has nothing to do with invalidating everything else about what those same people thought about morality or traditions. Coming to the realization that slavery was wrong didn't invalidate everything our founding fathers believed either. But they were clearly wrong on that issue.