Of course a Christian can do that, and quite obviously so:
1. Just as God made an eternal covenant with David and made him a forerunner of the Messiah Jesus, knowing from eternity that he would have a man killed in order to have his wife, whom he was already sleeping with.
2. Just as God gave Moses the Ten Commandments and responsibility to deliver, lead, and teach the Jews and write five books of the Old Testament, even though he had committed murder.
3. Just as David respected King Saul and wouldn’t harm him when he could, saying he was “God’s anointed”: even when Saul was trying to kill him. God consented to let Saul be king, even though He knew that he would eventually sin and fall away from the faith, and die in that state.
4. Just as Jesus said “render unto Caesar what is Caesar’s” when Rome was about to kill Him and His Christian followers.
5. Just as Jesus chose St. Peter as His first pope, even though He knew he would deny Him three times.
6. Just as the Church approved St. Paul to be an apostle and the premier evangelist of all time, and writer of about half of the New Testament, after he had persecuted and killed Christians.
7. Just as St. Paul showed deference to the high priest who had him struck at his trial, because he was the high priest (though not even a Christian), and because Paul cited the OT passage, “you shall not speak evil of a ruler of your people.”
8. Just as God allowed Solomon to be Israel’s third king, and to build His temple, even though Solomon, too, went astray later in life and may have also died in sin, having accepted foreign religions.
9. Just as Romans 13:1-5 (RSV) states:
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.  Therefore he who resists the authorities resists what God has appointed, and those who resist will incur judgment.  For rulers are not a terror to good conduct, but to bad. Would you have no fear of him who is in authority? Then do what is good, and you will receive his approval,  for he is God’s servant for your good. But if you do wrong, be afraid, for he does not bear the sword in vain; he is the servant of God to execute his wrath on the wrongdoer.  Therefore one must be subject, not only to avoid God’s wrath but also for the sake of conscience.
10. And because the alternative (the Democrats) is a party that favors childkilling, sodomy disguised as supposed “marriage”, chaos at the borders, being soft on crime and terrorism, illegally weaponizing agencies like the IRS, FBI, and CIA to attack people and try to undermine a legitimately elected President, fights against freedom of religion and speech, and holds a host of other positions directly contrary to the Christian faith. Supporting Trump (once the actual facts of what he believes are known) entails very little that the faith opposes, or at the very least, far less conflict with the faith than voting for Democrats does.
Scripture is what ought to guide us in this, not our partisan biases or groupthink hysteria.
It’s fine (biblically speaking) to take an anti-Trump position position, as long as one consistently opposes Moses, David, Saul, Solomon, Paul, Peter, the Jewish high priest post-Christianity, and the Christian-persecuting Roman government also not having legitimate power (contrary to Jesus and Paul in Romans 13), and not able to be honored in that capacity by God or men.
Where folks got this silly idea that a President has to be a canonized saint in order for us to vote for him or broadly support him (whereas apostles and kings and popes had no such requirement), I don’t know. If that were the case, we could never vote for any of them at all. But the Church lets us vote for the relatively better choice of two or three.
Exchange on Professor Janet E. Smith’s [public] Facebook page:
David Eric Ashby: The argument shifts part way through from “can you be a good Christian and support Trump?” to “You must as a good Christian support Trump.” I agree with the former statement, so long as you are not also supporting those policies which are too brutal such as child separation at the border.
Me: Obviously, we won’t agree [with a President or candidate] on every jot and tittle, but that’s always the case, so it’s self-evident.
I would say that when the choice was Trump vs. Hillary, as it was in 2016, that Hillary’s views were simply too inconsistent with Christianity to vote for, whereas Trump’s were far less so. So it’s not absolute, in your second sense, but it was a very clear, stark choice and division: an easy choice indeed.
In my opinion, the abortion / SCOTUS aspect alone made it almost unquestionable that a pro-life Christian would have little choice but to vote Trump (assuming a choice of two and not three, which is another discussion, and assuming the civic / Catholic duty to vote).
(originally 7-21-18 on Facebook)
Photo credit: Solomon Building the Temple (1554), by Marten van Heemskerck (1498-1574) [public domain / Wikimedia Commons]