How rude is "naff"?

Princess Anne famously told photographers to Naff off- so it is by royal appointment

Naff is a formal way of avoiding to pronounce the F-word.

It is usable in all situations involving fuck except the actual intercourse itself.

How rude it is depends of course a lot on the intonation and the circumstances but it is usually mild (especially considering how common fuck is nowadays). It is definitely less rude than fuck.

Here are a few entries from the authoritative Partridge dictionary of slang. Note how naff is used as a substitute for fuck in such expressions as "naff of" or "naffed up".

naff adjective vulgar, bad, unlovely, despicable; generally contemptible; when used in gay society it may mean heterosexual. Theatrical and CAMP origins but the actual derivation is disputed; possibly an acronym for ‘not available for fucking’, ‘not a fuck’ or ‘normal as fuck’; or a play on the military acronym NAAFI (Navy, Army and Air Force Institutes) as ‘no ambition and fuck-all interest’; otherwise it may originate as back slang for FANNY (the vagina or the buttocks), a shortening of ‘nawfuckingood’ or in the French phrase rien à faire (nothing to do) UK, 1965

naff used as a euphemism for ‘fuck’ (in all senses except sexual intercourse/to have sex) UK, 1977

naffette; naffeen adjective vulgar, bad, despicable, unlovely. Polari; CAMP variations of NAFF UK, 1992

naffing adjective used as a euphemism for ‘fucking’. Extended from NAFF UK, 1959

naff it up verb to spoil something UK, 1981

naff off verb to go away. From NAFF; made very familiar in the UK during the 1970s by the prison-set television situation comedy, Porridge, written by Clement and La Frenais. Perhaps the social highpoint of this word’s history was during the 1982 Badminton Horse Trials when Princess Anne (now Princess Royal) asked the press, ‘Why don’t you just naff off?’ UK, 1982

It's not that widely used any more, but isn't in any sense obscure. It seems to be considered fit for print and broadcast in "quality" media. Over all, not considered rude (beyond indicating something is in poor quality or taste), notwithstanding any etymology.

In my neck of the woods (SouthEast UK), naff almost exclusively means uncool, tacky, unfashionable, worthless silly, lacking taste. I must have heard it used thousands of times by hundreds of different people, and on a "rudeness" scale it's no different to any of those synonyms (i.e. - it's a bit slangy, but not at all "rude").

When Princess Anne told some photographers to "Naff Off!", it was much-reported at the time. I never knew of that usage before then, and I haven't heard it since except in parody of that royal original. I've always assumed that was just a very local idiom used only by a small (albeit exhalted) upper-class social clique.

Naff originally comes from the underground language called Polari. This was used by gay people in the 1950's in London's Soho district to converse, without outsiders understanding what was being said.
The original meaning of NAFF was therefore a gay abbreviation of Not Available For a Fuck. It ha since been hijacked for other use.

Naff is not particularly rude, but it is slang and so I wouldn't expect it to be used in writing unless it is being quoted as direct speech or unless the writer is using a slangy and colloquial register.