I've been testing this iRule with Internet Explorer, Edge, Firefox and Chrome. All these browsers seem to be working fine. Only Chrome seems to do things a bit differently and is showing a login prompt for a split second, but it's working.
How to use this snippet:
The screenshot below shows an example of an Access Policy that uses either Kerberos or SAML authentication.
The first agent in the policy is an 'Empty Agent' which will read the session.custom.domainjoined variable to determine which authentication method to use. The session.custom.domainjoined variable is set by the kerberos_auth_or_fallback_auth iRule.