Oddly I consider hide armor expertise badly broken (con barbs have plenty of other ways to stay on their feat and their AC was never bad), the avenger with this new feat is just a tiny bit too high (one point, IMHO).
Well, HAE is not limited to barbarians either. It's only OP in conjunction with Barbarian Agility ( so I'd say that it's more the latter that's OP ) whereas a shaman with HAE is perfectly fine.
In addition, since we're discussing a game where we have an expected range of AC/level, it doesn't really matter how many feats it takes to reach the expected AC: as long as the result is within a certain range, it doesn't break the game ( overpowered at most, but not really broken ).
PS: for any class that isn't an avenger or a monk, UA is strictly worse than Leather Armor Proficiency. Either you think that LAP is OP as well, or Unarmored Agility should be fine

It seems to me that rather than having a problem with Unarmored Agility and Hide Armor Expertise, you have a problem with Improved Armor of Faith and Barbarian Agility
