Mr Berners-Lee surely won't feel offended because the person addressing him isn't a [UK] royalist?
Most of her subjects do not complain. Some of them think we should have done away with such notions of reigning over other people already.
FWIW outside celebrity circles it is often considered quite gauche to insist on such pompous titles.
If you insist I'd be happy with calling him Professor Berners-Lee (even assuming he doesn't still have an active official professorship). If you want to talk about proper titles then is Sir Berners-Lee also rude when it should, by the right of HM EIIR be "Professor Sir Berners-Lee" [when spoken]?
If you're worried about recognition I think Mr Berners-Lee is not lacking in that department and was already party to the Queens inner circle as a holder of the Order of Merit which appears to be a far greater royal honour than a "mere" KBE. He has my utmost respect, if you doubted it.
Increasingly and to the point of arguable totality, such titles are bestowed by popularity, committee, and HM Government. Damned shame, since it would mean more what it should were it not given to celebrity riff-raff for 'services to sport'.
I digress. You say it's fine as a non-'UK royalist' to use an improper title; I say I bet most of the world doesn't use even Mr, and I'd do my utmost to pay proper respect to local custom and any honours.
For example, I'm not Catholic, but I would of course refer to Pope Francis; not 'Mr Francis', or anything involving his birth (as opposed to regnal) name.
Pope is a high office, and Francis is his chosen name. It would be rude of you to call him by his birth name; it would be rude of him to insist you call him "Your Holiness", although you probably should if you're visiting the Vatican.
You are clearly free to call him whatever you want, but I would advise you to be honest enough to realize that you're projecting your feelings about royalists onto him, and not calling him what he has chosen to be called.
If a person is an MD, professor, and such then that's totally acceptable. If the designation is "the Queen says you have to call me sir now" I don't really see what business it is of the Queen's or that it's more respectful to recognise a person because "the Queen smiled at them" than recognising their actual work/effort as fellowship of a learned society does.
It's an anachronous system of nepotism; bleurgh. What's not to like./s