Macs are not less compatible. If they are, it's not Apple's fault, but the fault of the person creating something for only one device.
Yahoo Mail Beta has been written by the guys at Yahoo to be only compatible with internet explorer. I didn't know this previously (I use my own email system), but it's entirely Yahoo's fault. In fact, I can't believe that a product being recently developed is made only for IE!! That is shockingly bad.
I'd strongly recommend not installing IE for macs though. It's old and support for it has been discontinued. Have you tried installing
firefox for the mac and seeing if it works on that?
Finally, you could move over to some system where the developers have some brains and have developed it for multiple browsers, i.e.,
gmail?