The public site sets a first-party session cookie when you submit a form, so the security token and any error message can be shown. The admin area uses a session cookie to keep you signed in.
These cookies are required for those features. If an analytics measurement ID is added in the website settings, the analytics provider may set its own cookies. Until that ID is saved, the site does not load an analytics script.
You can block cookies in your browser. Forms and the admin login will not work if the session cookie is blocked.