Is not Christ our example?
Should we not follow that example?
Christ was unconcerned with the political system He lived under.
He had bigger fish to multiply.
Shouldn't we?
Christ had a different purpose and mission from the Father than we do. When his was finished he was taken from this earth while he prayed that we be left here. So while I am in full agreement that we are to follow Christ and he be our example. This is not exactly a apples to apples comparison.
Paul would be however, Paul said follow me as I follow Christ. Paul was a citizen of Rome so he would have had the right to vote. We have no clue if he ever did or not vote on any issues that Roman citizens would have voted on. However, citizenship does have rights. Paul used them and had no problem using his rights under the political system.
When he was jailed with no trial he had no problem letting them know he was a Roman and they had no right to jail him. He then embarrassed the rulers that locked him up by demanding they come and release him.
He also appealed to Caesar as was his right and we can in Acts see how he using this right, it put him before kings and authorities to declare Christ.
So I would say getting involved or not getting involved as Christians would be a matter of conscience. So I would say for Christians to violate their conscience would be wrong. I would also think that the ones who do involve themselves see themselves as the stronger brother. I would also say that those who don't involve themselves see themselves as the stronger brother.
So with both sides seeing themselves as the stronger brother the bible lets us know that we then should not give offense to the weaker and let them be to serve God as their conscience dictates.