Hi Jim! Welcome to WikiTree!
There are several levels of privacy on the WikiTree. Since we collaborate to improve the profiles, we do try to keep the privacy settings as open as possible so that others can add their improvements. Some details about living people are here: https://www.wikitree.com/wiki/Help:Living_People and general information about Privacy settings are here: https://www.wikitree.com/wiki/Help:Privacy
For DNA and cousin connections to be activated on the WikiTree, the profile Family Tree has to be accessible by the program, so I most often use Private with Public Family Tree or Private with Public Biography and Family Tree for living individuals. If an individual is published on a public access record, such as the 1940 census, I use these Private with. . . settings so I can still see their cousin connections on the WikiTree. If there is no public record, I anonymize https://www.wikitree.com/wiki/Help:Anonymization the profile by naming the person Anonymous LastNameAtBirth as a placeholder. (Please see my brother, husband and dau on my profile: https://www.wikitree.com/wiki/Cooper-1 for examples)
However, if that is too much information for a family member, the profile can be marked Private. I do not enter children on the WikiTree, but those that do should set the privacy as Unlisted.