In a recent interview, Caitlin Jenner has said that she now supports marriage equality 100 percent. In the past, her position was more equivocal. So this represents a substantial change of heart for the conservative Republican. And remember, she is a conservative Republican!
Some people may say that, well, Caitlin Jenner is trans. Of course she would support marriage equality. But that's so not true. I know that plenty of LGBT people, usually older ones, who are opposed to marriage equality. In fact, in my experience, age (being a millennial) is a much better predictor of support for marriage equality. Even conservatives in our generation are likely to support marriage equality. In Jenner's generation? Not so much.
I think that Caitlin Jenner's recent change of heart could have something to do with her recent experiences, however. In the past two years, she has been frequently in contact with the LGBT community and its voices. In other words, she has had plenty of proper exposure to the arguments in favour of marriage equality, exposure that other conservatives of her generation usually don't get. And from my experience, (no offense to opponents of marriage equality), most people, progressive or conservative, would come to support marriage equality if they are properly introduced to the arguments and encouraged to really think about it. It's the same reason many millennial conservatives also support marriage equality.
It shows that marriage equality sits well with most people's conscience, and there is nothing within conservatism that is inherently incompatible with it.