Hi, and welcome.
I don't know your history or your fiance's history, so I can't say whether your parents' opposition to your marriage is based on something other than the fact that he is in recovery for alcoholism. I don't know whether he might have done terrible things to you when he was drinking. I don't know how long he's been sober.
That said, I married my first husband when he was one year sober. He had wrecked my car driving drunk without a license. Today, he's been sober for 36 years. He's a great dad, and in spite of our divorce he and I remain good friends. I often say (only partially joking) that my family thinks more highly of him than they do me.
I know many, many people who are alcoholics (I'm eight years sober, myself--my alcoholism developed a bit later in life), and I know many who have stayed sober for years/decades, and some who have stayed sober for a very long time and have gone back to drinking. There are never any guarantees.
The bottom line, though, is that you must do what is right for you, and you can't control your parents' attitude toward him, or the marriage. I'd suggest that you carefully consider what their concerns are, though. And if he's very newly sober, maybe wait a bit until he's been sober for at least a year. And if there's actual abuse in your history, keep in mind that alcoholism and abuse are two separate issues--putting down the drink will not necessarily alleviate the risk to you.
Have you educated yourself about alcoholism? If not, you should definitely do that before making a lifetime commitment.