Translation:Today, you cannot put on that red tie.
It means more, "One must not", but taking into account the fact that we don't live in the 1890s, "You cannot" is a better interpretation. In Japanese personal pronouns are almost always implied and not directly stated, as it is a high context language. This means you'll find a lot of sentences that aren't explicit in their meaning. Hope that helps!
While I agree with your point, I thought I should mention that -てはいけません wouldn't be used in the example you gave.
-てはいけません refers to not being allowed to do something, as opposed to not being able to do something; a subtle difference in English which commonly uses "can" for both situations, but uses different verb structures in Japanese.
In this situation using the following would be more common both meaning "I cannot wear that red tie" (feeling of...it just cannot be done)
With of course the many various polite/casual iterations being possible also.
One may argue if you spilled something on it that you COULD techincally still wear it and instead should use a sentence more reflecting the lack of desire..but...thats for another time.
What about the use of その? I think that pretty much implies you're talking to someone other than yourself who is either holding the tie or already wearing it. Am I right? Of course, it could be that said person is showing it to your as an option for you to wear, but I don't think that would be the first interpretation that comes to one's mind when reading the sentence.
I'm in my room getting dressed for the day, my gf is helping me, pointing out different ties I could wear. She points to one on a tie rack (adjust distance in your imagination to work with sono vs ano), "what about that red tie?" 「その赤いネクタイ?はどう？」I say to her 「今日は、その赤いネクタイをしめてはいけません。」I then explain to her that I can't wear that red tie today because I will be working at a career fair of a university who's main rival's color happens to be red, and it would be frowned upon. 「だって、今日はバークレーのキャリヤフォーラムに行く。そこで赤い服はだめだよ」
Yes? But only if you were being very adamant to yourself. It sounds odd that someone's internal monologue would be in such formal terms.
I'm not a native speaker, but I imagine that a Japanese person would normally remind themselves by saying something more like 「今日、その赤いネクタイはダメ」 or 「今日、その赤いネクタイはいけない」