It seems that it hasn't become much easier to visit Mount Athos than it was decades ago, and if you happen to be female, it's evidently impossible. But there is a way to see Athos from the sea, which should be enough for most people who aren't obsessed about Byzantine history and Orthodox monasteries (although these are very interesting), and that is to take a cruise alongside the Athos peninsula, making many monasteries perfectly visible from the ship. These cruises can be easily arranged in the tourist areas of the Chalkidiki Peninsula, and usually take in a break in the pretty port of Ouranopolis.
I don't really understand why the area was also inscribed as a natural site, since I didn't notice any particularly noteworthy natural monuments, but Athos' importance from a historical, political (an autonomous community for almost a thousand years!), religious, and cultural perspective is undeniable.
Nevertheless, I hope to be able to see Athos from the "inside" sometime in the future when they relax the rules. Until then I think I won't count it as a fully visited WH site.