"It tastes bad."
Subject-verb agreement. When the subject is third person singular (as "it" is in this sentence), the verb typically ends in "s."
Completely serious question: do Duo's English courses not teach subject-verb agreement? I ask because I've explained this three separate times in the English for Japanese speakers section because others also didn't understand why the verb sometimes ends in "s." This is something pretty important in English so it needs to be taught clearly!
I don't know the technical terms like KagayakuSeiza does, but here are some similar examples where the S gets added:
It runs well.
That looks good.
And a slightly more complicated example: He lets the animal go.
Third one is slightly more complicated because there's the word "let(s)" as in that sentence, but also "let's" as in "let us". You'd never say "He let's the animal go" since that wouldn't make grammatical sense.
But yeah, basically I think it comes down to what KagayakuSeiza said? I think if you can say something does something, then you generally add an S to the verb instead of adding "does" to the sentence. So, "It tastes good" is the same as "It does taste good". The main difference is that "does" is usually for the sake of emphasis in such sentences (e.g. "Whoa, this does taste good!").
Yes, there are plently of situations; the phrase in and of itself isn't considered rude (after all, it uses です which is the polite copula).
Largely, think of the same situations where you could say "It tastes bad" without offending someone, e.g. commenting to a colleague about the free lunch provided by your company or giving a review of a drink you made from every available option at a self-serve drinks bar (don't judge me; we've all done it).
Alternatively, as suggested by @KagayakuSeiza in the top comment thread, this phrase can also be used like an interjection à la "Oh-uh, this is bad", and so the considerations for its rudeness are exactly the same that interjection as in English.