I have been through the phone support, the chat support, had T-Mobile AND Google on the phone at the same time. Still no answers from T-Mobile.
First let me explain what I do. I teach continuing education night classes that are in various locations all over the country. To run my PowerPoint presentation I use a Chromecast plugged into a projector, my phone as a wifi access point (hotspot), and my tablet with Powerpoint. I push the presentation from the tablet, through the phone, to the Chromecast.
Everything works great until there is an update for the Chromcast. T-Mobile has the needed ports for the updates BLOCKED! My Chromecast becomes useless until I find a wifi network I can attach to, factory reset the Chromecast, reconfigure the Chromecast for the available network, update the Chromecast, factory reset it again and then configure it to my phone. This is a pain in the neck! The first year using the Chromecast updates over T-mobile's network worked fine. The last 8 months they don't!
Why are the needed ports to do updates blocked on T-mobile's network? WHY? Blaming Google for this doesn't cut it! Telling me that the Chromcast is 100% compatible with T-Mobile's network when it isn't doesn't cut it either!
Oh man, I wish I had a better answer for this. Unfortunately I don't have any good news or any true insight for you. It would likely need to be something resolved on Googled side.
This apparently isn't the first time something like this has happened to Chrome Cast users, I found this https://support.google.com/chromecast/forum/AAAAt7PFQG4c3Mc0GdJFYk/?hl=en which is a similar issue and the resolution wound up being a patch by Google.
I'm not sure if you've tried their support forums. But it looks like at least in that case a resolution was found!
Manage your T-Mobile account