Can a fitness app require HealthKit authorization? I don't see any mention of things related to this topic in the App Store Review Guidelines.
HealthKit authorization
Not sure if you are asking about App Store policy or how to implement this authorization in your application? It would help if you could expand on your question in another comment.
If this a question more on the policy of using Healthkit, there are several mentions of this in the App Store Guidlines.
https://developer.apple.com/app-store/review/guidelines/
Specifically, "HealthKit should be used for health and fitness purposes and integrate with the Health app." from section 4.2.1. Also under the 5.1.1 section, which mentions about the Health Data Collection and Storage. If you need help implementing this, please see the class reference I've posted below.
Here is the class reference for the HKHealthStore:
If you want to create a fitness application without HealthKit, that is fine. However, if you intent on using HealthKit API, you will need to implement the authorization be presented to the user.
Hope that helps!