Okay so i've encoutered this problem myself and i was so frustrated by it that i had to find a solution. AND I DID.
The controller input is where the game fails, you dont need to buy a new controller you just need to tweak soms settings, first lets go to the ALC tab (advanced look controls)
This is the way you need to play the game if you dont want to experience any sensitivity bugs.
Keep the Deadzone tab to own preference, the lower it is the more control you have, also if ur controller is very old you might experience stick drift then just bump it up until the stickdrift is gone.
Outher treshhold, now this is were the bug comes from, bump it a little bit higher then recommended because the game doesnt read the input u give on the controller.
Response curve (own preference)
Yaw speed/pitcher speed (look sensitivity)
Also put to own preference
TURNING EXTRA YAW, this is also were the game bugs the sensitivity if you turn this al the way down u dont experience the sensitivity bug anymore, but u turn slow AF and we dont want that. Try to find the sweet spot for it and set it to recommended, the keep on bumping it down until the sensitivity bug doesnt occur anymore.
For me this was the trick to fix apex and now i can finally enjoy the game again. If ur on ps4 and u have the same problems, ill be happy to help you in the firing range to fix this problem.
My psn:karpvlees
Just send me a friend request and type a message about apex sensitivity bug and i will help you as good as i can.
Sorry if my english sucks, not my native language.
Peace
