I have tried several variations of the following:

UserInfo ui = new UserInfo();
ui = UserInfo;
ui.Profile.SetProfileProperty("Email2", txtEmail2.Text); 
ui.Profile.ProfileProperties.GetByName("Email2").Visibility = UserVisibilityMode.AllUsers; 
UserController.UpdateUser(PortalId, ui); 

I have also tried ProfileController.UpdateUserProfile(ui); 

During debug if I drill down to the value it is correct but it does not change the value in the database.

It does change the value in the database if I change both the Email2 value and its visibility.

Anybody have an idea what is wrong?

Rather than updating the profile property definition or the user you need to update the the user's profile using the following static method of the DotNetNuke.Entities.Profile.ProfileController:

public static void UpdateUserProfile (UserInfo user)

In addition to updating the user's profile in the database, it also forces a clearing of the user cache for the referenced user.

Apparently setting the visibility using that method does not work.  You can update it straight in the SQL table --  I created a Linq DataContext & updated it that way.  Here is what I did to get it to work...

UserInfo ui = new UserInfo();
ui = UserInfo;

ui.Profile.SetProfileProperty("PropertyName", txtPropertyName.Text.Trim());
ui.Profile.ProfileProperties.GetByName("PropertyName").Visibility = UserVisibilityMode.AllUsers;  

LinqDataProviderDataContext dc = new LinqDataProviderDataContext();
//Loop thru and find the properties that are dirty
//if dirty then use Linq Datacontext to update the visibility property
foreach (ProfilePropertyDefinition item in ui.Profile.ProfileProperties)
{
    if (item.IsDirty)
    {     
        
        dc.ProfilePropertyVisUpdateSP(item.PropertyDefinitionId, UserId, (int)item.Visibility); //uses SP below to update

    }
}

DotNetNuke.Entities.Profile.ProfileController.UpdateUserProfile(ui);  //update the profile
UserController uc = new UserController();
uc.UpdateUser(ui); //update the user


Here is the SP:

CREATE PROCEDURE [dbo].[ProfilePropertyVisUpdateSP]
    -- Add the parameters for the stored procedure here
    @PropertyDefinitionId int,
    @UserId int,
    @Visibility int 
AS
BEGIN
    -- SET NOCOUNT ON added to prevent extra result sets from
    -- interfering with SELECT statements.
    SET NOCOUNT ON;

    UPDATE UserProfile
    SET Visibility = @Visibility
    WHERE UserID = @UserId AND  PropertyDefinitionID = @PropertyDefinitionId
END