Here is an example about how a disagreement about gay marriage could be problematic. First of all, “gay marriage” is rarely the only thing two people disagree on. If you disagree on the very definition of marriage and whether or not it’s ok, you probably also disagree on some other big issues, in particular, those related to faith.
Keep in mind that the purpose of your marriage is twofold - one, for the spouses to help each other get to heaven And two, to accept the children that God gives you and to raise them in such a way as to help them get to heaven.
I don’t know you, so I am going to assume that you are Catholic and that you are young enough that marriage will likely lead to children. So let’s say the two of you get married, and have children. You understand your obligation to help your kids get to heaven, and you know that committing mortal sins (without repentance and confession) is a really good way NOT to get to heaven. So when you start teaching your children about the truths of the universe and about right and wrong, you are aware that what you are teaching them impacts their ability to live a holy life and get to heaven. It is a heavy responsibility. Now, imagine that there is someone else in your children’s lives, teaching them the exact opposite of what you are teaching them. That person is telling them that right and wrong are mixed up, and that the Catholic Church can’t be trusted to be an authority on right from wrong. By teaching your children that “gay marriage” is ok, that person is probably also teaching them that in general, truth and morality are more about what seems right to the individual, or what feels good, than the absolute truth. So even if you don’t have any gay children (who would obviously be quite directly affected by this disagreement), you do have children who are learning how to discern between right and wrong, in part, based on how you teach them about gay marriage. And there are a lot of decisions in their lives that will be based on their foundation of how they view right and wrong and truth. And as I said, gay marriage is never the only disagreement, but one detail related to a whole host of issues about truth and morality.
I don’t know if this is hard for you to imagine, but in case it is (it was for me before I had kids), I will tell you - I have kids, and I desperately want them to understand and accept their faith. I desperately want to know that I am giving them the best possible foundation that would allow them to make the right choices in their adult lives to get to heaven. When I see people undermining that, I’m not just mildly annoyed. I see someone trying to keep my kids from getting into heaven. When I think about what is really at stake, which is my kids eternal lives, I am so much more aware of how important it is for me to give them that foundation. This isn’t just religious babble, it’s the real deal. And the stakes are high. When I look at my young kids, and imagine the possibility that they could go to hell, it is a horrible, terrible feeling. I know I can’t control it completely, but when I look at it this way, I am SO motivated to give them the truth and to not let them be taught wrong.
So back to your kids. You are working hard to give them that foundation. But if your wife is opposing you on basic and important issues, it isn’t just a disagreement. Instead it becomes an inability to give your kids the foundation of faith that is so vital to their ability to understand truth and live moral lives.
That said, I did make assumptions about your age and your own faith. If you are beyond childbearing years, then this is not an issue. It WILL still be your duties to help each other get to heaven, and you may still find that there are other, deeper conflicts that you have, which cause you to have more difficulty with each other than you now realize. But those are more manageable if you are not responsible for forming the minds and souls of your children.
As you can see, I would advise any young Catholic considering marriage, to remember how important it is to be married to another person who shares your deepest values and who sees truth and the world, and God and salvation the way you do. Which means that if “gay marriage” divides you, odds are strong that there will be a deep divide. Which can be difficult for a couple, but devastating for the faith of a child raised in that divide.