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. :-(((((