When you install a Go or Fly app on Android, in order to use that app, you are granting that app wide access to your phone. It requests access to the microphone, camera, location, storage, network settings, etc. None of that is unexpected for what the app needs to do.
When you couple that with the ability of DJI to update the code in the app without permission or review from Google, that opens the door to your phone being accessible to bad actors. This is how malware operates on Android; it's not the usual behavior for a legitimate app.
DJI gave its Android apps the ability to update themselves without going through the Google Play review process. This is probably the prime reason why they removed their drone control apps from the Google Play Store, and you now have to sideload their apps on Android.
It doesn't take DJI doing something bad to make this very sketchy. If they are hacked and a malicious party gains access to a phone with the DJI, the potential exists for that device to be used for illicit surveillance.
This is less of an issue on iOS, because Apple doesn't allow dynamic code updates or sideloading and has tight restrictions on 3rd party app stores.
This is a similar rationale for the current US investigation into TP-Link routers. It's not that TP-Link is inherently evil; it's that their security is so horrible that it's an easy target for bad people using TP-Link products to run botnets.
DJI could resolve some of this by making its control apps open source. Allow people to take the code and make their own versions that could be installed.
- Security issues could be addressed and patched without DJI shooting the messenger.
- Organizations that need tighter security could make versions that were completely locked down. These apps wouldn't be publicly listed in the app stores.
- Other features could be added.