Mounts now auto-switching the PS4 hotbar – can this be stopped?

[Exitthisway]

I'm on PS5 but this should still work and may be helpful to anyone who is still having this issue:

Character Config -> Hotbar Settings -> Cross (You'll have to tab over twice to this)

Under General Settings, there are a number of boxes ticked in this order:
1. Enable cross hotbar.
2. Always display cross hotbar.
3. Display hotbar help.
4. Use pet hotbar.
5. Use pet hotbar for mount actions and fashion accessories.
...

Turn the fifth option 'off'.

I was having this same issue and this is what did it for me.