They do not contradict each other.
Conservatism, for all it's BS about low taxes, small government, family values, etc... is really about who runs society and how it is structured. Think about it. Reagan, the prior modern vision of conservatism, grew government by 3 times the size. He cut taxes, but only on the wealthy, and shifted the tax burden onto the middle and working class. He raised taxes 11 times, but not on the wealthy. He just reverted back to pre New Deal thinking where the rich were rich, and everyone else was on their own. He maintained the racial animus that conservatives tend to have, though he was better at hiding it than Trump and today's conservatives. Poor white people were never really attacked by Reagan and the modern Conservative movement. The image of the "welfare queen" was specifically a Black woman and the "young Buck eating lobster", at no time in history was a young white man called a "young buck". Conservatives believe that there is a natural order to society and that wealthy, White, Protestant Christian, Men, who have been in charge of most European countries and the United States; are naturally the ones who should be in charge. Anything that maintains that order is fair game.
The extremists in that Conservative ideology move towards fascism. Trump has fascistic tendencies. As conservatives moved toward the right, he began to fit in more comfortably, to the point that he is the leader of the Republicans and of the Conservative movement. At the end of the day Conservatism is not a set of policy planks. It is a belief system that holds at its core, that certain people should be in charge based on certain characteristics. It is the same basic ideology that was proposed by Edmund Burke and Joseph DeMaistre in the 1700's with minor tweaks about just who should be in charge. They just replaced monarchs with Capitalists.
= new reply since forum marked as read