How do you handle finding out something about your spouse or mate that you find despicable or disgusting? What do you do now?

That is a very difficult question to answer. In the first instance, there must have been factors, probably many, that attracted you to that person. The question poses, without stating, that there is a single issue that revolts you. Is that issue sufficient to blind you to the issue/s that attracted you to them?
If the answer is that their "disgusting or despicable" trait bothers you, then you should front them and talk about it. However, if that trait breaks the criminal laws, Walk away.