This is very similar to a previous bug report but I wanted to clarify that it happens regardless of hotbar 1 being hidden or not.

The setting Pet Hotbar Auto-display Settings (under Character Configuration -> Hotbar Settings -> Pet Hotbar Display Settings) has three options:
1. Display both pet hotbar and hotbar 1.
2. Display only pet hotbar.
3. Display only hotbar 1.

Setting the option to either 1 or 3 allows for hotbar 1 to be automatically replaced by alternate hotbars such as mount actions, chocobo skills in Gold Saucer's chocobo racing and Mech skills in Rival Wings.

After switching to any other HUD layout and switching back, the Pet Hotbar Auto-display Settings will be reset to option 2, "Display only pet hotbar", in which case entering chocobo races or mounting a mount with skills does not replace hotbar 1 with the alternative hotbar.

Date & Time: Always
Frequency: Always
World name: Every World
Character name: Any Character
Retainer name: N/A
NPC name: N/A
Monster name: N/A
Class/Level: Any Class/Level
Party or solo: Both
In-game time: Any
Area and coordinates: Any

Steps to reproduce:
1. Set "Pet Hotbar Auto-display Settings" to the first or third option, apply/save setting
2. Switch HUD layout to another one. At this point the "Pet Hotbar Auto-display Settings" automatically changes to option 2.
3. Switching back to the original HUD layout will result in it having its "Pet Hotbar Auto-display Settings" changed to option 2 as well.