First, who says it's grammatical?

Second, who says only British speakers don't use it?

And, third, it's neither grammatical nor colloquial; it's a spin, or play on Bob Dylan's song
Everybody must get stoned.
The pronoun
everybody is indefinite. It refers to a broad group of people, a group that has little specification, and so it doesn't work with modal
mustn't, because in the negative that modal requires a subject that refers to a specific person. Consider this. The pronoun
somebody, like
everybody and
anybody, is indefinite, but if we make it definite, that is, specify the person it refers to, then it works with negative
must. Like this,
Specific: Somebody I know mustn't take drugs.
Non-specific: Somebody mustn't take drugs.
Does that help?