Villagers can't pathfind through fence gates even when the player can. Not sure if this is a limitation of how their pathfinding works or a bug.
Seems to be the same issue with iron doors.
If you make a path with 2 trapdoors on each other, they are trying to get through it by weirdly jumping.
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can confirm in 1.21.4

can confirm in 25w04a

I think this is cause they think that the fence gate is a full block, when in reality it isn't. All mobs think the same way for trapdoors and that's why trapdoors are used in mob farms.

@unknown yeah it could be, just tested with iron doors too.. But Interestingy if placed two trapdoors they are atleast "trying" to get through it
[media]
Duplicate of MC-21109, fence gates next to each other, while enough room to house a villager hitbox, is 2 solid collision boxes next to eachother, matching that report.