Hello gmd1107,
Thanks for that info and for choosing the Apple Support Communities. If I understand correctly, you are unable to set the Find My app to allow location access to "Always" as expected compared to your friends. First, make sure your iPhone is up to date, as the updates contain stability fixes that can resolve issues like yours, as well as important security updates to keep your iPhone safe.
Update the iOS software on your iPhone, iPad, or iPod touch
Next, you may have to reset your location settings by going to Settings > General > Reset and tap Reset Location & Privacy. Then open the Find My app and see if the "Always" option is presented, and then contact Apple if you need any further assistance.
About privacy and Location Services in iOS 8 and later
Contact Apple Support
Cheers!