A creature that "flickers" under the purveyance of Containment Priest is not going to be able to come back to the battlefield.
Ichorid and Narcomoeba are gonna have a bad time if they try to enter while Containment Priest is around!
Cascade tells you to cast the card you exile, so Containment Priest doesn't interfere.
Dryad Arbor can never be cast from your hand (or anywhere), so it can never enter the battlefield with Containment Priest around!
Containment Priest can only affect things that enter while it's already in play. So anything that enters at the same time, like with Show and Tell, will be able to enter normally.