My boyfriend and I have complete opposite communication styles, are we doomed?

Styles are overrated. This idea of personality styles communication styles is over rated and overdone. Most people express themselves differently depending on where they are, who they're with, and what's going on. But developing flexibility and acquiring new tools helps you deal with people in more situations better. Learn from each other. Listen to each other. Let love be more important than style.
Maybe, maybe not. The old saying that opposites attract has validity. It's a matter of balance when opposites attract. Maybe you both can learn each others language. It takes patience and acceptance but what a balanced and powerful team you could become if you accomplish that. Obviously you are attracted to each other so it's worth a try.
Keep the lines open. Communication styles are much less important than learning to talk about difficult issues. Real problems and challenges arise in all relationships and partners disagree. Successful couples are imperfect in many ways, but what sets successful partnerships apart from those who fail is that they figure out a way to talk about important and difficult issues. Good luck!