Would a red dwarf star resemble our own Sun at sunset to an observer on a nearby planet?
Your question may ulitmately be about the physiology of the eye, which is off-topic here.
The spectrum of the Sun seen low on the horizon is quite different to the spectrum of an M-type red dwarf. The reason that a red dwarf is red, is not just that it is cool, but that there are great chunks of the spectrum that are absorbed by molecules in the photosphere of the star. These molecules start to form when the temperature of the photosphere falls below 4000 K.
In contrast, the Sun has an almost continuous spectrum all the way into the ultraviolet, with relatively narrow absorption lines caused by atomic species in the solar photosphere. This is then modified, mainly, by Rayleigh scattering, which smoothly scatters blue light out of the line of sight towards the Sun.
Whilst any sort of spectrograph or prism could distinguish these differences, whether your eyes could is another matter. So whilst it is conceivable that the colours would appear similar for some particular angle above the horizon, the detailed spectrum would be quite different.