the government remembers you for jury duty if you have a license so dont sweat it. as for voting registering as a republican in a blue state…yes. because local politicians can very well be republican as can state politicians and you probably want to vote in those primaries.
also…as an aside…if you register to vote and vote then you have a right to complain about your politicians and teh state of politics in teh state. you did your part so you can be dissatisfied. if not…then no one wants to hear you because you have no right to complain about something in which you took no part.