I suspect that some people that have posted their issue is "fixed" were not having the same type of bluetooth keyboard issue that the original poster described.
It sounds like I'm having the same problem as the original poster. We have a Cisco wireless network as well and when I try to connect our iOS 7 device to our guest network that has a logon splash page, we are unable to type anything into the username or password fields.
With iOS 6.x we didn't have any issues.
So far this problem has occured on every iOS 7 device, iPad 3, iPad 4, iPad 4, iPhone 4, iPhone 4S, iPhone 5S, etc. I've tested with a Logitech Keyboard Case, Logitech K810, and Apple Bluetooth keyboard.
The keyboards are all working everywhere else, except the wireless splash screen. I can go to Chrome or Safar browsers and type just fine there. On the Cisco wireless splash page, I can't intpu anything in the username or password prompt, but the media keys still work, I can see the volume go up and down, adjust the brightness, so the keyboard is definitely working.
I called pple support and it seems they have not heard of this problem, though they are investigating this for me. I also contacted our vendor that implimented our Cisco network solution at my site. They also say they've not heard of anyone having this issue.
So this sounds like a combination of iOS 7 and the Cisco wireless splash page not liking each other. Though I'm baffled what Cisco could have done that would prevent Bluetooth keyboards from using their splash page and why it started to be an issue only in iOS 7.