When a player rides a mob, the player's model moves as needed. But if you dismount the player and mount him on the mob, then the player will be in the real position of the entity, and not in the position of the model with interpolation. In the video, I showed two cases: 1) without teleporting the player (the player does not dismount). 2) the player is constantly rotated by the command by 1 degree around the Y axis and mount on the mob.
(Sorry for my English)

Commands:
load

kill @e[type=minecraft:rabbit,tag=v]
summon minecraft:rabbit ~ ~1.5 ~ {NoAI:1b,Tags:["v"]}

tick

execute as @e[type=minecraft:rabbit,tag=v,limit=1] at @s run tp ~-0.5 ~ ~
execute as @a[tag=r] at @s run tp @s ~ ~ ~ ~1 ~
execute as @a[tag=r] at @s run ride @s mount @e[type=minecraft:rabbit,tag=v,limit=1]