Now that is odd. Reinstalling the current OS, or upgrading always clears all current cache data, which I thought may have been a possible issue. If you create a new test account and login to that, does it do the same thing?
No, I don't see how that could possibly make a difference, either. No matter what mail app or webmail portal you click on the invitation from, it's going to be the same URL. Where the email is or comes from has zero control over whether or not a browser will display the page correctly.