I am running a game and we have two different shape shifting characters.  Offhandedly in the game last night I mentioned that I thought that the threshold they had just crossed without invitation would suppress at least some of their powers.  With most things I look to the RPG books and then to actual books themselves.  In fact, Your Story  but I can think of a time where any of the alphas or hexen wolves shape shifted behind a threshold they were not invited behind... Nor were they ever in a position to need to.

Personally after looking through the rules, I'm just inclined to have thresholds suppress or block supernatural abilities outside of True Faith abilities outlined in the books, starting with the active and offensive powers first and the last powers are the defensive and passive abilities.  Some exceptions for things like Casandra's Tears, and other powers where the power is physically part of the creature, for instance if an Ogre is strong enough to get past your threshold he's going to be very strong still.

I'm just still struggling with this since I know there is some disagreement in my gaming group on this issue.