I do agree that humans tend to notice things that are different from themselves. If a white person blushes, gets sunburnt, gets an awesome tan, has an acne outbreak, has psoriasis, etc, I'll notice their skin. (Forgot to say: I'm white. Pasty white person.) If someone isn't white, I'll notice their skin tone and based on that plus other physical features will mentally tag an ethnicity -- black, Indian, Asian, Tongan, Maori, whatever. I don't deliberately or even consciously do it, but I know I do it.
I can't imagine a story featuring Unimportant the White person:
Unimportant entered the store. Three people were standing in line by the cashier. An older black man with thick grey hair fumbled his credit card into the reader. Behind him, a brown-skinned Indian woman readjusted her sari. At the end of the line lounged a woman with banana-flesh-coloured skin who was plopping her sixth? no, seventh, box of condoms into her basket.
So, IMO, describing every character's skin tone would be -- out of character. But, equally, writing a story set in a multicultural society where every character is white is -- unrealistic.