You ---- worry about your appearance - you look fine.

A) mustn't

B) don't have to

As a native speaker, which one would you use?
Mustn't is ok in British English (the favourite saying of little old ladies is 'mustn't grumble').

I see them as having two different meanings (slightly).

You mustn't worry about your appearance. An instruction. Perhaps you are nervous about making a speech and fussing about things. Someone is giving you advice and includes this. Another, I'd say more common use in British English, is to dismiss a valid concern. If someone spills a glass of wine down their dress at a party they might be reassured that 'now you musn't worry about your appearance, just enjoy the rest of the evening'. Or if someone looks a mess and can't do anything about it they might be told this - it's a way of saying, yes your appearance could be a cause for concern, but we don't want you to be worrying about it, never mind, just ignore it and get on with what you are doing.

You don't need to worry about your appearance. There's nothing wrong with your appearance. You look good.
Great, Nona, nowEmotion: smile
pls tells us where do you see

You shouldn't worry

in relation with the above two, in BrE.

I see it as a substitute for mustn't, just a bit softer, still a touch of advice/instruction in it.

You needn't worry

even softer. No instruction in it.
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DiamondrgYou ---- worry about your appearance - you look fine.

A) mustn't

B) don't have to

As a native speaker, which one would you use?
B, in my book, is better than A for the simple reason that as a Yank, I don't use the negative of 'must'. I might also suggest "shouldn't".
I agree with Philip. And the question almost seems designed for students of BrE, in which case, I think the test makers might expect "mustn't". I'm not sure, though, so let's wait for more responses.

Modal expressions separate into the modality and the residue.

Modality: must, should, can, have to ...
Residue: the rest, i.e., worry about your appearance, in this case.

With negation:
have to
+ negation negates the modality; must + negation negates the residue.

You are obligated to this: not to worry ... (mustn't)
You are not obligated to this: to worry ... (don't have to)

(They actually mean two different things.)

 nona the brit's reply was promoted to an answer.
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 Marius Hancu's reply was promoted to an answer.