Besides the fact that any passage worded in that precise manner would be clearly and instantly recognizable as a translation into Spanish, and not an original text written in Spanish, I think the word "authoritarian" carries much different meaning within the two distinct cultural contexts.

The English phrase “authoritarian conservative” within the context of American democratic life, and the Republican-Democratic political dichotomy and practice, isn’t nearly as strong as "el autoritarismo" to the ears of a Spanish speaker. Especially anyone who had at one point in their life suffered under a brutal and repressive military (or communist) dictatorship, for instance Franco in Spain, Pinochet in Chile, Castro in Cuba or under any of the various Central American military dictators in past years. Let's be honest - Republicans are bad but they're not exactly leading death squads into our houses at night (no, they just arm and train Latin American soldiers who...oh, let's not go there, it's a whole other discussion...)

I rather like the following definition:

El autoritarismo es una modalidad del ejercicio de la autoridad en las relaciones sociales, por parte de alguno o algunos de sus miembros, en la cual se extreman la ausencia de consenso, la irracionalidad y la falta de fundamentos en las decisiones, originando un orden social opresivo y carente de libertad para otra parte de los miembros del grupo social.

El término se utiliza para calificar a organizaciones o estados que pretenden conservar y gestionar el poder político mediante mecanismos no democráticos.

It actually sounds a bit nastier than some get-tough Republican candidate in a US election, and it's generally not an option that one would choose willingly.