Should people have the option of not participating in their government?

Yeah, why not? That's why we call it freedom. 

In my opinion it depends on where you live. In the US i believe that due to there being a right to having freedom of religion and beliefs, it would make the most sense to grant freedom concerning politics.  I wouldn't necessarily participate with the government as frequent if i was given the choice, but everyone's different. 

The majority of both parties voted in favor of the bill all senate republicans voted in favor of the bill