I have an iPhone 5S that I upgraded to iOS 11 and now it will no longer connect to data when I have Wi-Fi and Bluetooth turned off.
My Carrier is T-Mobile and I have Wi-Fi Calling enabled.
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Disable Wi-Fi Calling. When you disable Wi-Fi and have Wi-Fi Calling enabled it wont connect to cellular data. Not sure if this is related to how T-Mobile Wi-Fi Calling is, or if it is an iOS issue.
Try to reset your network setting from your iPhone 5s by going to: Settings > General > Reset > Reset Network Settings.