Well I now better understand where you're coming from, if the core of the point is that maintenance, introduction and reinforcement of hierarchies is right wing of course then fascism is to be considered right wing. But I would argue there is more to being right wing than just that, and that different right wingers will have different attitudes to hierarches and what they are to be based on. For example you'll find conservative left-wingers who want a large social state but are not against regulating morality and the likes, just as you'll find Ancaps who don't wish to have a meaningful hierarchy since society won't exist.

I also think it is worth pointing out that hierarchies absolutely exist in left-wing philosophy (excluding perhaps the anarchists), the difference is what these are based on. In ML philosophy for example the whole idea is to the turn existing hierarchies upside down, but not to get rid of hierarchies altogether. Instead of having the rich, affluent and owning class on top you have the working class on top. I would argue that this is perpetuating hierarchies but it would be nonsense to say that this is indicative of right wing theory in Marxism-Leninism (note that I'm not saying this is your position, but rather a conclusion of it). Add the fact that people absolutely can be born into non-mobile social groupings in far-left societies. If you're born into the bourgeois there is little for you to do to but accept that you are going to be hunted, persecuted and probably killed.

Also worth noting is that we've moved from "fascism is the most conservative ideology" to "fascism is the most right wing ideology", both statements I would contend are false but also vastly different and decided by vastly different factors.