It is doubtful that the update would cause that, unless, of course, it wasn't a true update (done through the phone settings) and instead the device was rooted to make it accept the newer Android version. If that is the case, then you would be better served unrooting the device and going back to the version the manufacturer allows.
However, if the device was not rooted, and this was a normal update, then try starting up the tablet in "Safe Mode" and see if the headphones will work in there. If they do, then there is something on the device that is restricting it. Bad app, virus, malware, etc. You would then need to find the problem and remove it before the device will work normally.
To get into "Safe Mode" please do the following.
1. First turn off the tablet.
2. Next press and hold "Power" until you see the manufacturers logo on the screen, then release the power button.
3. "Quickly" press "Volume Down" and hold it for few seconds until you see the message "Safe mode: ON" or something similar.
4. If you wanted disable it, simply repeat the steps above, and you should see "Safe Mode: OFF" rather than on.