When I change the exercise goal on my Apple Watch 7, the exercise goal on my wife's Apple Watch 7 also changes. Why is that? How do I get that to not happen?

Is it possible that you and your wife are sharing an Apple ID? If so, stop. Each person should have their own Apple ID to keep things separated and to prevent mixing of content. Make sure that each family member has a unique Apple ID - Apple Support There are ways to share with Family Sharing. Family Sharing - Apple

Do you and your wife share Apple IDs? This is not recommended.

Make sure that each family member has a unique Apple ID - Apple Support

(Sorry about the duplicate, Chris)

Create a new Apple ID