Explain the potential consequences of allowing businesses to refuse service to certain groups based on personal beliefs or conscience.
Yep, every business owner who hates gay people for whatever reason could put out signs saying "No homosexuals allowed" or "Help wanted: homosexuals need not apply".
All they'd have to do is claim their conscience is violated.
Conservative Christian groups would launch campaigns claiming businesses that didn't discriminate were anti-Christian and anti-family-values.
The people backing this baker want to shove gay people back in the closet.