Using the mobile site, I was able to join as if the site was in public beta. I thought you had to be invited to join.
Anyone can visit the Area51 proposal page and click "Visit" :)
It's only private inasmuch as it's not indexed by Google or anything, so it gave us a few weeks to put some content on and figure out the lay of the proverbial land.
Welcome to Monero SE! Everyone is definitely welcome now.
I committed prior to private beta but am under the impression people can still join now if they use the visit link on the Area51 site.
Public beta should be starting in about another week.