It would have been good if there was a way to lie to the app. For example if it wants access to your contacts, it could get a blank list.
Of course, it is much easier to not use such apps in the first place. Uber is not alone in doing this and personally I take it as a signal of how I'll be treated as a customer.
For the most sensitive things like location, contacts and photos, it prompts for user permission.
There's a lower category for things like background processing, you declare to Apple that you want to use them, and they are enabled by default. Some of them can be disabled by the user after the fact.
Then, there's things like internet usage which there is no permission system for.
Unless you have a limited cellular data allowance, or pay for data by actual usage. iOS allows you to disable cellular data for certain apps. It would be great if it could somehow figure out when I'm using a mi-fi when abroad, and treat that wifi access point as 'cellular'.