Some parents may even feel relief that it is now out in the open. Feelings are just feelings. In themselves they are neither right nor wrong, they just are. Your feelings need to be acknowledged and owned, not denied and repressed. Remember the feelings you are experiencing are healthy and are actually part of the healing process.
Mothers have different reactions to fathers about the homosexuality of their child.
Loving your child is just loving your child. It does not mean that you are approving of their every decision. Some guilt is genuine. Owning up to involvement is not accepting blame. The child is responsible for their own sin before God.