Some Republican movements have been authoritarian, but an effort to prevent people from saying that which is undesirable is definition authoritarian just as much if not more so. I don't know what example of authoritarianism you would offer as characteristic of the Republican party, but I'm sure you could offer more than one or two. That's because both political parties must push authoritarianism because both must accumulate authoritarian power to stay in the game, lest they be overpowered by the opposing party.
While constituents, we the people, agree on most points like personal freedom, individuality, respect of human life, and liberty etc., politicians of both parties, out of necessity, must paint their opponents as the authoritarian regime, set on revoking personal freedom and individuality, and devaluing human life.
If you dislike either party, it's not because one is more authoritarian than the other. It's because we lack the mental capacity to retain all the information that makes up the world around us, and must therefore make easier to process, generalizations to survive; Republican, Democrat, grassroots, mainstream, Black, Hispanic, White, etc. And it's obviously no secret that this necessity to generalize is very much exploitable.
What you don't like about the Republican party is all the things that are also the Democratic party, but only in a generalized view that the opposing parties' electorate has succeeded to exploit in your mind.