The sun sometimes appears pure white after rainfall, how can this be explained?
When it rains the raindrops nucleate around aerosol particles of salt, dust, clay, soot, dimethyl sulphide, etc. In addition a falling raindrop may pick up any particulate matter that may be in its trajectory. The net result is that rain 'scrubs' the atmosphere clean. Without all these polluting particles to diffuse different wavelengths of the spectrum, the eye perceives the 'full spectrum', which the brain interprets as 'white light'.

In addition, you are quite correct that the eye's response to light, and to what constitutes 'white light' is very variable, depending upon light intensity, extent of blue sky vs. cloud, direction relative to the sun, reflections from buildings, the sea, etc. and other factors.