This is not a bug report so I moved this question to the developer forum.
I just tested logging into demo.mojoportal.com using Chrome browser on my iPad and it worked just fine. If you experience a problem with your own custom login page then look to how or if you are setting a cookie, I have no way to diagnose it for you.
As far as I know cookieless authentication in asp.net can only be configured by web.config and mojoportal will not be able to use that.
It is not something negotiated by the web browser.
I do believe web browsers can be configured to not accept a cookie, but nothing in mojoportal code nor in your custom code could overcome that if the browser is configured that way.