Is the new version of this code more difficult to read and understand than the original? How can it be improved?
Disclaimer: I'm not too familiar with C#.

The modified form has expressions that are a little too complex for me, but either would be ok. My only comment is that the initial comment line is screaming for some notice:

// Only add corporate AD domain if the user is a member of it.


Why not take all the tests and put them into a function?

if ( IsMemberOfCorporateDomain( Thread.CurrentPrincipal ) ) ...


Then, depending on how you both feel about early exits:

private bool IsMemberOfCorporateDomain( IPrincipal currentPrincipal )
{
    if ( currentPrincipal == null ) return false;
    if ( !currentPrincipal.Identity.Name.Contains("\\") ) return false;

    var domainName = Utils.GetUserDomain(currentPrincipal);
    return string.Equals( domainName, Config.AppsSettings.Domain, StringComparison.OrdinalIgnoreCase )
}