I refuse to allow my parents access to my phone history.
Do you think your parents would react poorly?
They would just blow things out of proportion and create unnecessary conflict
It's totally fine for you to want some privacy when it comes to your phone history. Unless they have good reason to do so, they shouldn't be able to access your phone like that whenever they want.
Also, I don't want them to know which apps I have or have ever used. I know they would get mad and they would tell me to change phone behavior.
It doesn't seem like you're doing anything wrong and it's wanting your phone history and app use to remain private is completely reasonable. I'd stand your ground on this one and let them know you will not allow them access.