How is 'reasonable' different from 'rational'? And don't both these terms beg the question of ultimate ends and/or values?
I think "reasonable" means people do things for "reasons", even if those reasons may be logically wrong; it takes into account the fallibility of man. I see "rationality" as more of a platonic form, under which the things people do are strictly logical—but this is often not how people behave.
The reasonable person principle doesn't ask you to assert your conception of reasonableness on everyone—it's just to trust that when you're interacting with someone, they aren't trying to actively harm you or do something that they don't think is "the right" thing to do. What you believe to be right may differ from them, but the key is not to hold grudges, feel personally attacked or angered by the things other people do. Instead, just accept that, given their point of view, conditioning, and environment, people do things for reasons that makes sense in their experience; and what may seem as "unreasonable," may just seem so because you lack the requisite information to assess their thought processes.
I remember hearing this advice from Stanford prof John Ousterhout when I was taking his classes, and I find it to be profound—it echoes the same dogma of non-reactance that many in the meditation community extol. Check out the Four Agreements by Don Miguel Ruiz for a synopsis of what I mean, in which the author points out that when people do things that offend or hurt you, you have a couple options: either be vindictive towards them, and in turn make yourself feel angry and miserable for it; or withhold judgment, attribute any wrongdoing as a consequence of their life experience which you do not know, and don't let it interfere with your life and inner peace. In doing so, you can live a productive, happier life by not wasting time and emotional energy doting on the pain people inflict on themselves because of external stimuli, like the dysfunctional social norms we live under. That text is short, and while it has the occasional new-agey bs, it's almost entirely high quality content—if you're open-minded and ready to take it seriously.
It's interesting seeing Hacker News discuss these sorts of things, as many here seem to discount lifestyle choices like this very quickly.