well fwiw while spirits cant cross at all, some things can enter fine with no invitation so long as they dont have hostile intent. Fae being the main example. On the other hand wizards loose the bulk of their power regardless of their hostility. But then Shapeshifters like the Alphas can shift even when in a circle trap, so Im not sure if they'd be able to maintain their forms after such a crossing. It's really a species-specific thing, though Id use those three (Fae, Humans, and Spirits) as the measure and decide based on how similar they are to each.