I run a private IMAP server that uses a certificate signed by a private Certificate Authority (I created the CA in Keychain.app on my Mac and I then created the IMAP server's cert, signed by the private CA taken from Keychain.app).
A long time ago, iOS Mail app made it easy to get my mail by first warning about the cert, but then easily allowing me to trust the cert with a simple click.
On iOS 12.x, things got harder, but I was able to install the CA as a Profile, then go to Settings -> General -> About -> Certificate Trust Settings to mark the CA as trusted, and that allowed the Mail app to trust the IMAP server's certificate (via the private CA via the trusted profile).
I already had the CA's profile installed and trusted before upgrading my iPad Pro to iPadOS 13.0 (beta).
The upgrade to iPadOS 13 removed the CA's profile, so I re-installed the CA's profile.
The CA showed up under Settings -> General -> About -> Certificate Trust Settings as already trusted.
Nonetheless, attempting to read e-mail from my private IMAP server results in "Cannot Verify Server Identity" as if the server's cert is not being properly matched to the CA's profile. :-(
I am now faced with a pop-up, every few seconds stating, "Cannot Verify Server Identity" in the middle of anything I am doing on the iPad. :-(((((
Any solutions?
YAY! Workaround seems to be to delete and recreate the mail account after installing the private certificate authority! =D =D =D
Finally I can enjoy testing out the more interesting iPadOS 13.0 (beta) features, other than just the one of always hitting the "cancel" button on the "Cannot Verify Server Identity" prompt, every few seconds. ;-)