If you want to get a villager into the nether, you have to get it in a Minecart/Boat, get the boat/cart to the portal, then break it and let the villager travel through.

What's supposed to happen:

The villager takes a bit of damage then travels through, with the boat sometimes getting in too.

What happens instead:

The villager turns black with its head stuck in the portal ceiling, taking no damage. The entire game freezes for a moment, then the villager phases through the ceiling and lands on the ground, clearly still in the overworld. The boat always travels through, meaning the problem is with villagers specifically and not with general portal-entity interaction.

How to recreate:

Get a villager in a boat, drive said boat into a portal, then break the boat. It doesn't matter if there are any blocks around the portal.