Logging into apps using Facebook credentials always uses a browser - Is this avoidable?
This is by design. Separation of applications and processes on iOS is deliberate.

Interprocess Communication (IPC) on iOS

Interprocess-communication between iOS apps is particularly limited. Apple would argue this is a net benefit, as their customers are better protected from malicious behaviours that are difficult to detect during the review process.

Shared Credentials Between Apps

Apps created by the same developer, digitally signed by the same organisation, can share credentials on iOS. This is how the Facebook and Messenger apps can both know you are logged into the Facebook service. But other Facebook connected apps, created by different developers, can not.