Here's the main problem, we have been given the Bible to discuss. Discussion of the Bible is sensitive enough all by itself. People feel strongly about various doctrines and Biblical positions.
We have our hands full trying to calmly, and kindly discuss the things of God with one another.
Once we add something political to our discussion of the Bible, we have people on one side of the issue, and others on the other side of the issue. As soon as we state our political position, no matter what it is, about 50% of people immediately become defensive. They've been trained, by the world, and politics is a worldly subject, to retreat to their side of the issue.
Now, let's say, an individual, after having a political discussion in which he laid out his position on things, then wants to put forth a Bible study on some subject. Or, just wants to share some Bible truth with others that he finds is comforting or encouraging. Some people, due to the previous discussion on politics, are not going to receive the things he says. They will shut their ears to it.
Well, you might say, people shut their ears to Biblical things and there is nothing you can do about that. The Word of God the Bible is offensive to the unsaved people of the world. That's true. However, God emphasizes in His Word that we (the child of God) are not to be the cause of the offense ourselves. If we are the cause of the offense then we have done wrong.
Personally, I have beliefs and strong feelings about the way things are done or run politically also. Everyone has their views on things. But, I keep them to myself because I know that making known my personal views would give opportunity for some to be offended. Anyone uncomfortable with the Word of God, or the faithful doctrines coming forth from the Word of God, could then seize upon something said about politics or something else, and use that as a reason to go away from the truth.
A person might say, "Well, you're a teacher, and you have to watch out for that, I don't." We're all servants of the Lord. And it’s not just teachers that need to be concerned about being a personal representative of the Lord Jesus Christ and His Word, its all of us.
2 Timothy 2:23 But foolish and unlearned questions avoid, knowing that they do gender strifes.
24 And the servant of the Lord must not strive; but be gentle unto all men, apt to teach, patient,
25 In meekness instructing those that oppose themselves;
Based on the passage in 2 Timothy 2, which speaks about the servant of the Lord being gentle, etc.. I've prayed a prayer for many years now, a prayer asking God that I myself not be the offense. If the gospel (Word of God) be the offense, so be it. But may it not be me personally that causes an offense to another person.
I think that's the main focus a child of God ought to have. Pray for the way things are going in government if it concerns you, vote in a way that supports your beliefs (one reason God's elect may get involved in voting is because it is private, we do not have to make our choice known, thus maintaining that position of not wishing to offend...). But overall, we leave the things of the world to the world. And we turn our attention to spiritual matters.