I suspect the problem is that Apple is being evil.

Why would the browser being non-compliant with standards (of which AJAX is not one, btw) cause Apple's server to send you to the same page repeatedly?

The browser does not say those things of its own accord, but because Apple detected the UA as not-approved, and sent you a different page recommending a different browser; if they won't let you past that, you'll probably need to change the UA reported to one of the allowed ones.
Or to try to get people to use Safari, perhaps.

(Have you tried any validation of Yahoo Mail? Without knowledge that it is standards compliant, it's not any better evidence that MicroB is the problem.)