The touch-responsiveness requires that Unity generate a camera-depth texture, which is dependant on the world's lighting. In worlds that do not have the correct lighting, you can add one to your avatar (note that this will automatically make your avatar rating "Poor").
Adding a Directional Light to your Avatar
Step 1: Left-click on your avatar, and select "Light -> Directional Light" to add a new light:
Adding a Directional Light
Step 2: Select the newly created light, and change the following 4 settings:
The Directional Light settings
Step 3: Confirm that the light is working by enabling "Show Contact Zones". If the lighting is not correct, a checkboard pattern will appear:
The checkerboard error pattern