I have T-Mobile as well, so understand your concern!
Unlocking the car (with the phone key) is not a concern. Yes, that works using BluetoothLE, so it's completely localized. However, you should carry your backup key with you anyway as occasionally the phone key is flaky for some people and on some software revs.
Connectivity through the app has been rock solid (provided my phone has signal anyway). I have experience with both Nissan LEAF and Chevy Volt/Bolt and outages there were far more frequent. In the past year I can only remember one or two outages with Tesla. I can live with that. And response time is immensely better with the Tesla...my wife can track the car real time vs. GM On-star where you send a request to locate the car and about 30 seconds later it pops up the current location.
I recently returned from a road trip where the car did lose connectivity twice. Of course most of the media streaming is over the data connection, so I did have to ride in silence for awhile (alternatively I could have played locally stored music on my phone via Bluetooth). Navigation continued to work in both cases just fine, but I lost the satellite view (I just got a grid instead). Now if I had STARTED navigation without data I can't say whether it would have worked or not. I do know that it downloads a pretty hefty map to the car every now and then, so it's possible that it has detailed maps locally in the car, but I'll let someone else confirm that. Tesla uses the AT&T network, which is fairly robust, in case that helps.
