The English translation here is really inconsistent. As Laszlo.Sc pointed out, the offered translation "Why do not you wear white clothes" is wrong. Furthermore, attempting to answer "Why do you not wear white clothes" is rejected and the user is suggested to answer "clothing" rather than "clothes". However, if a contraction is used, ("Why don't you wear white clothes") the answer "clothes" is accepted.
Yes, both are accepted here.
To my native AmE ear, "clothing" sounds a little more... maybe sophisticated? formal? ... than "clothes," but they are used similarly: "Why are your clothes so dirty" -- "Why is your clothing so dirty?" In the US, at least, "clothes" is probably more common in everyday speech.
Thank you for the declension scheme (which is the same as for nádraží). But while I can see what the plural of nádraží (train stations) means I have problems seeing what the plural of oblečení means, given that the singular already has a plural meaning.
Does the singular mean the clothing/clothes of one person and the plural that of several persons?
So if, e.g., František had bílé oblečení and so had Kateřina, would we talk collectively about their bílá [plural] oblečení?
Well, the plural for oblečení is really uncommon and seems to me a bit like sheeps or fishes in English. It refers to various kinds of clothing. It is unlikely to be used just for several items, but I am sure you will find an example of anything. Those items would have to be very different:
"(dva muži) ... postupně zapózovali v několika oblečeních včetně starověkých nebo pyžama a županů." "(two men) successively posed in several types of clothing including an ancient one or pyjamas and bathrobes."
My guess would be that in the singular, we might be referring to just one article of clothing. To me, using the word "clothes" or "clothing" to refer to one item is an odd concept in English, but maybe Czech behaves differently. (Or my guess is totally wrong.)
In any case, I think your question is probably better addressed by one of the Czech natives on the team!