Um, by examining the reasons they gave.
I suppose that it depends on what you mean by "rational". In particular, it matters whether you consider logically valid reasoning based on false premises (such as the premise "every interpretation of the Bible by my religion is true") to be rationality. If you do, then I concede, that it might be no change in rationality or even a change in the direction of less rationality.
On the other hand, if you consider rationality to be following a process that results in true beliefs, then believing that gay marriage is okay is rational and rejecting gay marriage is not, but to convince you of that I would have to convince you that the former is a true belief and it's probably impossible for me to do that.
"every interpretation of the Bible by my religion is true"
First, I don't think even most Christians at the time would agree with that as a premise. This about as accurate a caricature as describing someone's position as "every one of my beliefs is true". Second, as I have pointed out repeatedly in this thread even the atheists at the time rejected gay marriage.
but to convince you of that I would have to convince you that the former is a true belief and it's probably impossible for me to do that.
Why are you so convinced that is in fact a true belief since you don't seem able to produce any argument for it?
Suppose I told you that I knew for a fact that the following statements were true:
You’d think I was crazy, right?
Now suppose it were the year 1901, and you had to choose between believing those statements I have just offered, and believing statements like the following:
Based on a comment of Robin Hanson’s: “I wonder if one could describe in enough detail a fictional story of an alternative reality, a reality that our ancestors could not distinguish from the truth, in order to make it very clear how surprising the truth turned out to be.”1
1Source: http://lesswrong.com/lw/j0/making_history_available/ewg.