Depending on your iphone's settings, and what data you don't want Apple collecting, that could mean anything from turning off iCloud to not using iTunes and the App Store.
Basically, any app is likely giving Apple data on you. (Well I take that back. Apps will give some company data on you. But they won't necessarily give it to Apple. Obviously for full and complete privacy you would need to turn off any google, facebook and amazon stuff as well. Also any ancillary apps, like mileage meters, or health and wellness type stuff. A lot of games too now I think about it.)
This is very crucial and I really don't see any alternative services to the ones like Strava and RunKeeper for iOS.
Even an app that does the job w/o any social features would do (in fact I never use the social feature aspect of these apps)
2. stop using publication stuff (gamecenter) since that's literally public information Apple broadcasts for you
3. that's about it, the rest is various accounts information e.g. your appstore/itunes purchases, your retail stuff, repairs, … basically your files at Apple, the only way to request that Apple does not generate it is to delete your account (which the portal lets you, there's an option to nuke your account entirely and permanently) and stop interacting with Apple entirely, or at least in such a way that they can link things together (e.g. appleid when purchasing devices, that kind of stuff)
Just a small correction: although most of iCloud is definitely not E2E encrypted, a small portion, iCloud Keychain, is. It's a great way to sync passwords and secure notes across devices.
TLDR; if you're not actively asking Apple to store data for you, they probably aren't.