Been there, done that. I'm up in Canada. Years ago, our own supreme court struck down a legal provision defining marriage as "the union of one man and one woman." That was never replaced with anything, so any human being is now free to marry any other human being. It might even be possible to marry multiple people and commit bigamy, but nobody has really tested that yet.
If the US court strikes down California's law, it could open the door for a nationwide legalization of same-sex marriage.
So what's that got to do with asexuality? Well, as an asexual, I'm not gonna screw my spouse in bed, so I don't care what sex my spouse is. I'd be equally comfortable marrying a man as a woman, provided that s/he accepted there would never be sex between us. There are a million reasons to marry other than sex, including security, trust, financial comfort, companionship, and so on and so on and so on. You can even marry someone out of deep platonic love, as exists among some very close friends. My primary motivation for marriage would be so that, when I get old and infirm, there is someone to help take care of me and prevent me from being totally isolated the way so many old people are. I'd pick someone who is at least 15 years younger than me. Now, I only need to win the lottery first.
But seriously, it could be either a man or a woman. What do I care about their genitals?If there are other asexuals with my mindset, then things could get wide open in the US very soon, the same way they are here. I wish you guys the best of luck.