How do you ensure the privacy of your address on your Amazon wish list? Your public profile contains your (public) wish lists amongst other things. If you want to see what information you're putting out there, click "View your profile as a visitor."
To edit your privacy settings;
Hover over "Account & Lists," and click on "Your Account." Scroll down to the "Ordering and shopping preferences" section. Click the "Profile" link, above the social media preferences link. Click the link in the orange box to the right that says, "Edit your profile" then click on the Edit privacy settings tab.
You can select or deselect items individually such as public wish lists. You can also "Hide all activity on your profile," which turns everything off at once. To edit or delete any personal information like your name or address, go back to the profile settings page and click the Edit profile tab located next to the Edit Privacy settings tab.
When creating a list select “You” under “This list is for” to keep your address private. Some people also suggest using a P.O. Box address instead of a physical one.