A Familiar cannot use its movement to enter a hallowed area
This should be relatively uncontroversial. The hallow spell prevents certain types of creatures from entering an area. Familiars from the find familiar spell may be one of the affected types. Therefore, they cannot willingly enter the affected area using mundane movement (walking, flying, etc.)
A Familiar cannot be moved into a hallowed area with forced movement
This is a somewhat more involved explanation. Spells such as moonbeam, spirit guardians, and certain other area-of-effect spells, have an effect that apply when "a creature enters the spell's area." According to this answer related to moonbeam, forced movement does count as "entering the area", but having the area moved over you does not. Taking each of these spells to use the same definition of "to enter," that would imply that forced movement, such as a push or pull, cannot cause an affected creature to enter the area. If they could, then it would not track that forced movement also counts as "entering the area" of a moonbeam, etc.
A Familiar cannot be summoned/"appeared" into a hallowed area
We've now determined that mundane movement of any kind, willing or not, is blocked by hallow, but the question remaining is whether less mundane means - specifically, teleportation, summoning, or "appearing" (as find familiar calls it) - also count as "entering an area." Based on the plain definition of "to enter," this must be interpreted as yes.
Webster's dictionary defines "to enter" to include "to come or go into." A broad reading of these would therefore preclude any form of "going into" the area, be it by teleportation, summoning, or "reappearing." Some of these can be thought of as forced movement (what if the familiar doesn't want to reappear?), but we have already determined above that forced movement also does not work, so the difference in form is irrelevant.
Extradimensional Interference does affect this, but not in the way you might think
So the question this all brings up is how does Extradimensional Interference work if creatures can't enter the area in the first place to be affected by the interference? The key is that the entry-restriction effect and the "extra effect" of hallow are actually considered two separate lists, not one in the same.
From the entry-restriction:
First, celestials, elementals, fey, fiends, and undead can't enter the area... You can exclude one or more of these types of creatures from this effect.
Later, in the extra effect:
Some of these effects apply to creatures in the area; you can designate whether the effect applies to all creatures, creatures that follow a specific deity or leader, or creatures of a specific sort, such as orcs or trolls.
The spell gives you leave to make separate choices for each of these effects. So, the expected use case of Extradimensional Interference would be: the entry-restriction effect should exclude a creature that is desired to be bound by the spell, but the extra effect should include creatures of that type.