For one thing, there is the issue of abortion.
Let me explain that I'm against abortion. I'm even more against the idea of the government deciding who may or may not have an abortion. I feel no need to impose my values on the rest of society by force. Doing so is an authoritarian position.
Does the government have the right to decide who may or may not marry? I say no, most Republicans say yes. I'm a registered Republican, BTW, but they can't count on my vote. They have to earn it.
In fact, most of the time, I'll vote my conscience which leans strongly Libertarian on most issues.
Is there even one Republican who is in favor of a more rational drug policy? The war on drugs is another example of authoritarianism. Now, I'm not a druggie myself, mind you, but if someone else wants to smoke a little weed, what's that to me? Throwing them in prison is not the answer. As for the hard stuff, it's time to treat drug addiction as a medical problem, not a legal one.
There is the "Patriot Act", deserving of the Orwellian Doublespeak Award.
And the death penalty. Why is the party of limited government so ready to give the government the power of life and death, especially when so many have been proven innocent after having been convicted?
Of course, there are authoritarian planks in the Democratic Party's platform also, but you already know that.