There are two authentication token levels with Media Center: read-only and full.
The authentication tokens are used when communicating with Media Center via MCWS and some other instances.
The read-only token provides limited (read-only) access, so there are still several functions that cannot be done with a read-only token, typically, things that require writing changes to a library.
Disabling authentication sets Media Center to only obtain a read-only token automatically. You cannot obtain a full authentication token.
Enabling Authentication sets Media Center to require verification before obtaining a token.
Setting Read-only Authentication to Everyone allows the MCWS authentication call to obtain a read-only token automatically, no username or password required, while still requiring a username and password for a full authentication token.
Setting Read-only Authentication to Username and password requires a username and password to obtain a read-only token, which is different from the username and password to obtain a full authentication token. With this method, you can still have private access to Media Center, possibly for friends or family, without allowing them making any changes to the library.
Authentication impacts any device making MCWS calls, such as JRemote, Gizmo, Panel, et cetera, as well as Sync Library, which requires full authentication because this involves writing changes to a library server. It does affect content streaming because it uses an MCWS call, but the authentication is usually handled automatically. It doesn't affect how Media Center pushes media to other zones.