Apple should probably remove Safari since there's too much unmoderated content on the open web.

Apple doesn’t take any responsibility for websites. They moderate the App Store. Anything on the App Store is there with Apple’s blessing. That includes the content inside third party apps that is only created by its users.

Apple just don’t want to be associated with it.

And Parler doesn't take responsibility for user generated content. So how is that any different?

Parler takes some responsibility for the content in the app if they want to publish it on the Apple/Google App Stores - because the store policies demand that they do.

This is unrelated to legal responsibility. It’s an agreement between the owner of the App Store and the creators of Apps on it.