Have you ever been selected for jury duty? I haven't, so I can't speak to the screening process.
In cases of capital punishment I wouldn't be surprised if they screen out people who are against it, since it would be a conflict of interest. A jury's only purpose is to determine whether someone is guilty of a crime, not to weigh in on sentencing. Although I'm pretty sure sentencing comes later anyway.
Most likely, same as if a married woman were elected. Hillary Clinton said Bill probably would have been called First Gentleman.