One of two things happened:
Too much force was placed on the home button flex when it was being removed from the old display (this thing is pretty fragile) and caused the issue. If that happened, it is likely that the home button would not function at all.
The other possibility is that the replacement display has a defective home button flex.
one way to test this (assuming you still have a working LCD on the old, broken display) is to put the old display back on the phone with the home button and see if you get TouchID back. If your LCD is broken on the old display, you can probably find a nearby repair shop that would be willing to troubleshoot that for you.
If you find that you get TouchID back on a different display, then it is a parts issue, and your display should be returned for a replacement.
Best practice to avoid damage to the home button during repair is to never put undue pressure on the flex. pop the connector, gently push the home button up from the front of the display to separate the gasket from the display assembly, and very, VERY carefully use a pry tool to cut the adhesive under the chip to the right of the connector.