Here's another video, exactly the same as others have reported: https://www.youtube.com/watch?v=Z2DqHxEeanA
I found this thread with an apparently identical issue, only with tanks: https://www.reddit.com/r/battlefield_live/comments/8ez11g/after_3_updates_i_still_cant_deploy_a_tank/
This started some time after Apocalypse DLC, and the screwed up loadout mentioned in the thread above would actually make sense. I remember this started after the game crashed when squad spawning into a bomber on Air Assault as Support. Maybe the pilot died while I was spawning, because it looked like the game was suddenly trying to spawn me as pilot but with a Support loadout.
i5-3570k, 16GB, GTX1080. 100% repeatable across all maps and game modes. Can spawn as gunner or in other vehicles, but Pilot is an instant kick. Repair and reinstall are totally ineffective even after deleting all client-side configuration files.