The white/black/yellow/red race classification system is based on the Western race classification system. Wikipedia is not the best resource and definitely not the most reliable, but sometimes, you can find interesting articles about general topics.
Galastel, you mention on your own profile that you are from Israel. You have also mentioned that you speak English, Hebrew, French, and Russian. Hebrew is a Middle-Eastern language. Surely, you can find something in the modern Hebrew language about race. To my understanding, the Jews view themselves as one people or one race regardless of actual skin color. Maybe in your story, you may have a fantasy race, in which the fantasy race only puts people into two categories -- the civilized people and the savage barbarians.
Under those constraints, how do I describe my MCs' ("brown") skin colour? (Other characters can sort of follow from the MC's baseline and the MC's perception.) I have so far used "tanned", but that isn't right at all - it suggests that the character is naturally paler than they currently appear, which is not what I'm trying to describe.
First of all, I don't know what you are describing. Let me search for an image.
In my opinion, that man appears light-colored.
In my opinion, that man also appears light-colored.
In my opinion, that man also appears light-colored.
In my opinion, that man appears dark-colored.
"Brown" doesn't really work either, for the reasons explained above, and also because it's not really descriptive - so many shades of brown.
Assuming that you are a Middle-Easterner, specifically an Israeli, you can look at your own skin color and compare other people's skin color to yourself. If a person has lighter skin than you, then you will describe that person as "light-skinned". If a person has darker skin than you, then you will describe that person as "dark-skinned". If a person has exactly the same skin tone as you, then you will ignore the skin color, because your own skin color is the default.
You may also look into the Hebrew language and how it categorizes people based on skin color or race. Then, you use the Hebrew word in original form or in transliteration in your English manuscript.
And it would be strange, I think, to describe my MCs' appearance in exotic terms, since they're supposed to be pretty much the norm.
Language and culture come hand in hand. In many works of English literature, authors focus on hair color and eye color, because (1) the English language evolved from the English people, and those types of people have varying eye color and hair color so they use hair color and eye color to distinguish people, and (2) the focus on hair color and eye color in culture is embedded in English literature and language.
You may follow this literary tradition, focusing on specific color terms to describe physical appearance, or you may describe people in your Hebrew language and translate that literally into English. The Chinese language, for example, does have color terms, but there is no one-to-one translation with English color terms, esp. when describing people. For example, 黑 may refer to the color "black", the skin color of a Black person (idea borrowed from the West), or a dark-colored person (may be a dark-skinned Chinese person). If a native Chinese person has darker skin color, then that person may be described as 皮肤黑黑的, referring to the darkness of the skin color. 黑 in this context does not mean "black". It just means "dark". In addition, in the Chinese language, facial characteristics may be described without using color terms at all.
(It might be that I'm having a blind spot, because this is what I look
like. Since it's mine, it's just "skin" to me.)
Then use yourself as a reference point. Even if you don't use yourself as a reference point explicitly, then readers may still use you as a reference point. Sometimes, Chinese readers will take into account of the author's own personal background as a reference point. If the author uses specific regional Chinese terms in the story written in Standard Written Chinese, such as 伊 as a pronoun in literary/classical Chinese and vernacular Chinese, then the reader may take into account of the author's background and assume that the author is literally from that region in China. Similarly, J.K. Rowling is British. Her Harry Potter series unsurprisingly sets in the United Kingdom and has a lot of British cultural references.
This one is about describing a "white" character in a "non-white" setting, while mine is about describing the average "non-white" character in the same setting.
I can only speak from a Chinese perspective, because I am Chinese-American and bilingual in Chinese and English. In a Chinese context, I am quite hesitant in labeling a person as "Chinese" or "non-Chinese" based solely on appearance. I need to double-check on nationality or ethnic group affiliation. If a person is part of the Han people or 55 ethnic minorities in the People's Republic of China, then I'd consider that person "racially Chinese". If not, then I'd check to see if that person descends from the Huaxia people. Those people are also considered "racially Chinese". So, a person with blonde hair and blue eyes from England with no blood from the Hua people or whose bloodline to the Hua people is lost to history would be a "foreigner". I would also consider Sinophobes "foreigners".
Because if the characters were Caucasian, I would not have struggled to describe their skin colour, and I would have mentioned it in passing (one character being tanned from spending a lot of time outside, another having pale, almost translucent skin, etc.) so it's weird to avoid describing a different skin colour just because the frame of reference is not Caucasian.
Have you considered taking ideas from your Hebrew language? How would a Hebrew speaker describe a person in Hebrew?