Seems to me there was sarcasm from both sides, but let's put that behind us for now.
Our new login system is provided by Stormpath. From what the devs have told me, the iOS issues stem from Stormpath itself, which apparently does not play nice with iOS. We're currently in the process of working with them in trying to sort this out.
While many people might use mobile versions of Safari (I'm skeptical on that 1/3 of the mobile market number), Safari does make up a fairly small portion of our userbase here. Not that that is any excuse for not finding out about this sooner; believe me, there will likely be some kind of fallout from this, especially considering that the new login system was supposed to have been tested extensively and was even launched on our French and German sites first to make sure we avoided these kinds of problems as much as we can.
I'll report back when I learn more about the situation. In the meantime, I presume that Chrome and Firefox on iOS is still able to access the site, or at least, I have not heard any reports to the contrary.