Well, personally I’ve come to realize that I am, in fact, a Dane - it’s not something you just shrug off. I’m not sure I could swear full allegiance to another country just like that. (Also, Denmark doesn’t recognize dual citizenship.) I’m definitely holding on to my Danish passport.
I do try to spend time and money on the political process, to make up for my lack of voting. Not ideal, but it’s the best I can do.