Is "You don't have to come to the party" correct?

Why

Farah's starting fact is genuinely correct — in their POSITIVE forms, "must" and "have to" really do mean nearly the same thing: "you must come" and "you have to come" both mean coming is required. The moment you make them negative, though, they split apart sharply and stop matching. "Mustn't" means something is FORBIDDEN — not allowed under any circumstance — so "you mustn't come" means "do not come, you are not permitted to". "Don't have to", by contrast, means the OPPOSITE kind of freedom — there's simply no obligation either way, so "you don't have to come" means "coming isn't required, but you're welcome to if you'd like" — permission remains open, unlike "mustn't". Test: imagine actually showing up to the party after each sentence — showing up after "you mustn't come" would genuinely break a rule, while showing up after "you don't have to come" would be completely fine, since it was only ever optional. No, the two mean almost the opposite: "mustn't" forbids an action entirely, while "don't have to" simply removes any obligation, leaving the choice open.