Enabling airplane mode completely disables the cellular radio, so you shouldn't be able to receive any calls. However, Wi-Fi can be enabled again, and you can receive calls through your carrier via Wi-Fi calling. Did you check that Wi-Fi was turned off as well? When you turn airplane mode on again, it remembers your Wi-Fi and Bluetooth settings, so it could be that you accidentally left Wi-Fi on.
If the problem persists, it would be helpful if you could provide some more details. Your headline mentions flight mode, but later on you talk about disabling WiFi, LTE and Bluetooth. I don't know how to turn off LTE, but you could try turning off mobile data. I think this will make the LTE symbol disappear, but you will still be connected to your carrier and able to receive calls.