They both owned (or at least financially supported) bookshops in London.  McCarthy’s was Indica Bookshop (the basement was Indica Gallery, where Yoko Ono had an art show and met John Lennon).

Is it that they both inspired massive public interest in investigating a possible hoax?

I hardly need to expound on Voynich's side of this, not to this group.

For McCartney, we all know the "Paul is dead" hoax, right? From the rumor McCartney died in a car crash in 1966 to the backmasking on Revolution 9 from the White Album, which when played backwards sounds like "turn me on dead man", to John Lennon himself misleading the public by saying things like the "Walrus is Paul", conspiracy theorists and fans went searching for years for proof in many Beatles songs and album cover art, which in turn was covered by the media and analyzed by professionals with great interest and has led to many pop culture references to it. There are still some people today who think Paul really died in 1966 and that the person we know as Paul is an imposter. If you can believe it.

Well done Tavie.

Voynich had his bookshop on 1 Soho Square until (about?) 1904.
Nowadays, this address hosts McCartney's Music Publishing Company.

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(which I only found after posting the question) already makes the link.
The building at 1 Soho Square shown there was only built after Voynch moved
out.