The bronze badge is awarded on post number, so as long as the large majority of your posts aren't anon, it shouldn't make a great deal of difference.
I guess they decided to try and reward people who don't post anon, hence the anon votes not counting. And I suppose it does sort of make sense, that if the badges represent some kind of 'reputation signal' then only your visible posts should count.
I don't really know why they bothered though. As the Register forums are mostly about banging on about the subjects of the articles, I don't really understand why they even want a user reputation system. It'd make a lot more sense if people came here for technical advice. I suppose it's possible that this is a direction they want to head, now they've launched the non-article forums. Otherwise, a badge for 'long-term denizen of our forum' is understandable - for which bronze does the job perfectly - so why the rest?
I don't mind the voting, despite our jake's loathing for it, but I do agree that the badges are kind of pointless.
Although obviously, as one of the elite gold-badgers, I still look down on everyone else as the plebs they undoubtedly are...