Had this problem with a broken iphone 7 plus i purchased with a damaged screen. The phone worked perfect with the cracked screen including the home button and touch id , how ever when I replaced with a copy screen the home button and touch id both would not work so i put the parts back on the old original screen and they both worked. I then purchased a original refurbished LCD from a different part store and both home button and touch id worked.
This is hardware related.. for iphone 7/7plus i recommend using higher end LCD instead of the cheap copy. Also this problem can occur if you were too rough with home button itself so make sure to heat it up before removing from original lcd.