Testing in the most recent snapshot you can spectate minecarts again looked for old issues but they were marked as resolved.
Just noticed the same also applies to boats but boats don't actually glitch out when spectating.
MC-161304
Can spectate minecarts & boats (minecarts shake screen)
Resolved
Duplicate
0
NinjaPhenix
(Unassigned)
Unconfirmed
(Unassigned)
19w38a
Retrieved
Thank you for your report, but it is a duplicate of MC-99556