Hi DJScott2,
Thanks for posting. I understand you're finding your iPhone's Music app seems to be shuffling.
If you've verified that the Shuffle button is off and you're not tapping the Shuffle button at the top of your playlists/library, there might be a few things to consider. You mentioned Bluetooth connections; is your iPhone connected to a vehicle or other device when this happens? If not, that would be an unlikely cause, but you can check for Bluetooth connections by tapping Settings > Bluetooth. If you find any there, you can try unpairing them to see if that helps: Pair a third-party Bluetooth accessory with your iPhone, iPad, or iPod touch
To unpair a Bluetooth accessory, tap Settings > Bluetooth, find the device you want to unpair, and tap the info button 
, then Forget this Device. This will remove the accessory from the list of available Bluetooth devices."
If there are no Bluetooth accessories and you're running iOS 13.1 under Settings > General > About, you might try uninstalling and reinstalling the Music app as your next step. You may need to re-download any saved/offline content after: Delete built-in Apple apps on your iOS 12 or later device or Apple Watch
As a side note, you mentioned permanently disabling Shuffle; while that isn't an option, you can always send your suggestion to Apple here: Product Feedback
I hope this helps!
