Only repository collaborators can edit a public repository's wiki by default, but you can allow anyone with an account on your GitHub Enterprise Server instance to edit your wiki.
Wikis are available in public repositories with GitHub Free and GitHub Free for organizations, and in public and private repositories with GitHub Pro, GitHub Team, GitHub Enterprise Cloud and GitHub Enterprise Server.
On your GitHub Enterprise Server instance, navigate to the main page of the repository.
Under your repository name, click
Under Features, unselect Restrict edits to collaborators only.