Further to Joe suggesting that the screen protector doesn't affect the performance of the touch id I can only add my own experience.
I enrolled my thumb twice as per Joes video with screen protector on. The id worked erratically & sometimes not at all.
I was fiddling around with the phone & decided to just pull up the bottom of the protector away from the home button. The touch system worked straight away. I switched off completely & re started & tried again after initially entering PW after start up, worked time & again.
I took off that protector & cut another one short so not to encroach on the home button. Works very well & I'm pleased.
It's nearly 4 days since doing this & it's worked every time but sometimes outside it needs to be touched 2 or 3 times.
Now I know Joe used a plastic bag over his finger & it worked but is there any difference in the plastic of the bag & perhaps acetate in the protector? I don't know I'm not a materials engineer.
So all I can say, without the protector my phone works more or less as it should.