I wrote this message to an Objectivist facebook group:
Supporting Trump is the only realistic way to stop Hillary this year. Stopping Hillary, and judging her to be worse than Trump, seems compatible with Objectivism to me. (Note Gary Johnson's problem isn't just that he can't get enough votes to stop Hillary. His campaign has actually been less anti-Hillary than Trump's campaign.)
Let's look at some of the issues to see that Hillary is a lot worse than Trump:
Trump is pro drilling for fossil fuels, Hillary wants to put coal miners out of work.
Trump opposes the Iran deal and Obamacare.
Trump wants to enforce US immigration law and secure our border against criminals and terrorists.
Trump isn't running as Obama's third term.
Trump has promised to appoint supreme court judges from a pro-constitution list. They aren't ideal, but Hillary will appoint truly awful judges.
Hillary wants to make government way bigger, more intrusive, more rights violating, bigger budget, more agencies, etc. Trump isn't any kinda small government guy. I'd guess Trump views himself as planning to keep government around the same size, and will in fact grow it significantly. But he won't expand government as much or as enthusiastically as Hillary.
Trump isn't a literal traitor who would be in jail if not for government corruption.
Trump likes America and wants us to win. He mostly promises to do good things (that he probably won't live up to very well). Hillary dislikes America and mostly promises to do bad things.
Trump is not very religious and is kinda moderate. I don't approve of moderates, but it's still better than Hillary. Moderate means compromises, lack of principles, and (for a right winger) some leftist sympathies. Trump will compromise and sympathize with the anti-life left in a variety of ways, and will not solve most of our problems. But Trump will also do a few things pretty well, and we'll fall apart slower than with Hillary who has promised to destroy us in a dozen ways.
One of the issues where Trump is a breath of fresh air is opposing establishment politicians in both parties. Will he fix it? Nah. He'll try a bit and we'll be better off with him than with Hillary who will intentionally make it worse. Of the people on the ballot, Trump's the best one to vote for.