Testing for this issue in minecraft version 1.2.5, the FOV changes as expected. Turning through 90 degrees the FOV changes by 90 degrees too. When traveling diagonally the FOV changes correctly by 45 degrees. Even when looking backwards the FOV rotates as it would if you were traveling in a real minecart looking backwards.
Doing the same tests with the next release, version 1.3 snapshot & 1.3.1, the FOV gets hopelessly lost when the minecart changes direction.
According to https://minecraft.gamepedia.com/Java_Edition_1.3.1 there was the following minecart change:
"When riding a minecart that is currently on a rail, using directional keys will allow the player to slowly move the minecart in that direction."
I wonder if that's the change which introduced this issue?
This is a significant issue as it makes rollercoasters or long rail systems not so much fun in minecraft.
Probably not good for performance but running on Linux the following resolves the issue for me:
__GL_THREADED_OPTIMIZATIONS=0 minecraft-launcher