I also hate using public restrooms and needing to poop especially when someone else is next to me in the other stall.
I have a hard time pooping when someone is in the stall next to me so I don't use public restrooms anymore except to change my diaper when needed.
I actually don't even use a toilet anymore either at home or in public because I decided over 6 years ago to stop using the toilet forever and started wearing diapers full time.
I love to wear diapers because they feel great when dry, wet, pooped in etc.
The diapers are also very convenient to wear because I can be out shopping or doing anything else and don't need to stop and run to the restroom to use potty.
I just let go in my diaper both pee and poop and yes I do poop my diaper in public and change later as I love to walk around with poop in my diaper.