I imagine some of the early believers struggled with some of these same questions back when the Apostle Paul wrote to the Christians in Rome telling them to obey the governing authorities. He said,
Let every person be subject to the governing authorities. For there is no authority except from God, and those that exist have been instituted by God. Romans 13:1 (ESV)
They might have wondered if Paul truly understood who he was telling them to obey since the "governing authorities" in Rome were not known for being terribly friendly toward Christians. In fact, those same governing authorities eventually sentenced Paul to death and, according to Church tradition, did the same to most of the original Apostles. How could Paul ask the believers to respect and obey that kind of leadership?
Christian women run into this same issue all time. The Bible tells a wife to respect her husband, and yet many women are married to unbelieving men who live contrary to biblical principles and godly morals. I have often had women ask me how they can respect their husband when, frankly speaking, he doesn't deserve respect. But whether I'm talking to a wife or just someone, like yourself, who wants to know how he can possibly respect his elected officials, the biblical answers are pretty much the same, and they go like this:
1. Respecting authority is respecting God
Paul clearly states in the passage above that "...there is no authority except from God, and those that exist have been instituted by God." In other words, God is behind the authority of man. This means that when we respect and obey the governing authorities, we are respecting and obeying God as well. In the same way, when a wife respects her husband and his God-given role as leader and head of the home, she is likewise showing respect for God. When we obey the laws of the land, we show respect for the governing authorities.
2. Respecting does not mean agreeing
Like you, I have some grave differences of philosophy with the current administration. But if I were ever given the opportunity to speak face to face with our President I would certainly be respectful toward him. I would stand when he entered the room, I would speak using respectful words and language, and I would maintain an attitude that honored him as a human being and as my President. But I would also speak my mind and express to the best of my ability where I felt his administration and our nation has gone wrong. It is possible for people to express their differences while maintaining an attitude of mutual respect and civility.
3. Respecting doesn't necessarily mean obeying
The only absolute authority in our lives is God. No human can usurp that position, and when the Jewish Ruling Council attempted to do just that—demanding that the Disciples stop preaching in the name of Jesus—Peter and John respectfully replied: “Whether it is right in the sight of God to listen to you rather than to God, you must judge, for we cannot but speak of what we have seen and heard.” Acts 4:19-20 (ESV) So, they respectfully declined to acquiesce to the threats leveled against them, and made it clear they would continue telling people about Jesus, citing the fact that God's authority trumped that of any human court.
This is called "civil disobedience" but, for a Christian, it's never done for reasons of political or social awareness. It is only done as an expression of obedience toward God and only when obeying the governing authorities would require us to violate a clear directive from God. In other words, we can't pick and choose when to disobey.
So, I believe you can disagree (even passionately) with your government while at the same time maintaining an attitude of respect and honor. The two are not mutually exclusive.