We are seeing a similuar issue here at work on serveral devices.
Using Lotus Notes for mail and calendar
iPhone 5 and iPhone 5S
Running iOS 7
When an email comes in for a meeting invite if you click on the Date and Time in blue it will walk you through opening the invite in your calendar and then I can Accept/Decline without issue. If you click on the Invitation icon, which seems to be what users intuitively, in the the email then it freezes up the mail app., see image below.