Basically, all naturalized US citizens are required to upheld the same obligations like the citizens that born in united states. Voting in election and volunteering in political campaigns are considered to be the right/freedom of the citizens, not the obligation. You would not face legal punishments if you choose to avoid your rights, but you could face it if you avoid your obligations.
The British government led by David Cameron held a referendum on the issue in 2016; the electorate decided by a 3.8% majority to favour leaving the European Union.
