I'm working a Cleric-style subclass that doesn't get armor proficiencies but instead gets Monk-style unarmored defense.

Is there a way to remove proficiency via subclass (I don't think so, that's not exactly a mechanic within 5e's ruleset anyways)?
I have added the unarmored defense (Bonus - Unarmored Armor Class - Wisdom) but it allows shield stacking, which I don't want. How do I get it to treat shields as armor, and thus the ability turns off when equipped with one?

Luckily most of the Cleric Subclasses give their own armor proficiencies above and beyond the base class so that won’t be an issue. I’m not sure about the other issue.

Put up a link. I won’t matter that it’s private, a moderator would still be able to view it. They might have some idea how to help you fix it. (They have helped me fix sooo many homebrew issues.)

https://www.dndbeyond.com/subclasses/333218-war-monk

yeah not too stickler on losing any existing proficiency if I can get the features to turn off when they aren't met. 

Good luck. Hope they can help.