I am playing my first playthrough and chose to play as the Iceni faction. I ran into an issue where I upgraded a building, and am now receiving an error that "This building is not available to your faction." Is this a game feature, or some sort of bug?

It has made it so now I can only recruit the basic beginner type units. 

Feature.  Ordinarily, such buildings are those obtained by conquest that belonged to another faction and their building tree.  You cannot upgrade these; being Iceni; but you ought to be able to convert it to an Iceni building, else destroy it and then build upon the ruins.  (Be aware that even though foreign it might still convey a bonus upon your Iceni if left alone.)

I'll assume the bonus was being able to recruit foreign troops, and it got converted to an Iceni building?  So if it's causing you a major headache, you can restore a slightly older savegame to continue your playthrough with the foreign units recruitable - this time leaving that building alone.