How to access Google Hangouts chat on Mobile Safari?
Go to gmail.com in mobile Safari.
Hold the refresh button, and choose Request Desktop Site.

It will look exactly the same, but it actually did something.
Go up to the URL and delete everything after https://mail.google.com/.


The chat windows will be really small and barely usable, but you can at least read messages and probably send them too.



If you do things in a different order or try to use the button at the bottom of the screen to toggle between standard and basic HTML, you'll either end up going back to the mobile site, or you'll end up with the following error:


  You have been redirected to the basic HTML version because this browser is not supported. To use standard view please upgrade to a supported browser.


Ignore that message and try opening up a new tab and trying that same process above.