Did the Permian-Triassic extinction event's hydrogen-sulfide-tinted green skies shade out all non-green photosynthetic life on earth, leaving only today's mostly green plants and plankton?
Probably not. They could evolve again if it were a useful trait. See the Ghost redwoods for viable white foliage. We have surely had volcanic and cosmic winters since the PT extinction, that would have limited sunlight reaching the earth's surface. And would green skies favor green photosynthetic plants? What would a red sky do? A purple sky? An orange sky? Why do we have a blue sky today?
It is a very thought provoking question and I think it deserves to be answered in multiple stages.
Firstly, present day phytoplankton are not dominated by chlorophycean members instead, the most ubiquitous and dominant ones belong to Bacillariophyceae and are characterized by their brown/golden masking pigments.
Secondly, the colour green appears in plants and algae not because of the so-called colour of chlorophyll pigments associated with their chromoproteins, as they have no colour of their own. The ability of various chlorophyll pigments to reflect the green part of the visible portion of the electromagnetic wavelength, by absorbing the other spectra (based on the molecular arrangement of the radical groups), is what imparts specific hues to the organisms harbouring them. The absorption spectra associated with the ambient media composition and incident light intensity also play crucial parts in the final colour observed in aquatic media.
Thirdly, a green tinted sky due to the prevalence of H2S in the atmosphere would have meant nothing since the chlorophyll bearing organisms which ultimately phagocytotically and then endosymbiotically became incorporated and integrated within the ancestral bacteria like single celled organisms were within the aquatic realm and light attenuation within a few millimeter of the surface of the water ensures that the protophotoautotrophs never quite got accustomed to the atmospheric tint.
Fourthly, land plants evolved not before the Ordovician/Silurian periods as known to date and by that time the sky adorned a different sunset yellow tint. Hence land plants were not accustomed to anything green even to reflect that certain spectra for their own camouflage, if they ever needed one since there were nothing on land to munch on them.
Fifth point is in tune to your own question - every photosynthetic organism we see today has been here for at least the entire time period since the KT event and the sky has had predominantly been blue and we don't see any blue autotrophs, do we?
Thank you for an interesting question. I sincerely hope that my answer satisfied your query.
http://www.sciencemag.org/news/2018/02/land-plants-arose-earlier-thought-and-may-have-had-bigger-impact-evolution-animals just an addition - news about earliest land plants...