Mobs don't ride to the side of the minecart in the Nether.

This issue is invalid. For the villager to get into the minecart properly, you need to push it into the villager's hitbox, and not punch it towards the minecart.

See MC-47704. While punching a mob into a minecart does usually push the minecart enough to collect the mob, this doesn't work on deactivated powered rails since the minecart won't gain enough velocity. This behaviour is the same in all dimensions.