Your computer switches from Mac OS X to classic mode (Mac OS 9) because RealPlayer 8 or earlier is still installed on your system. When you click a RealMedia link, RealPlayer 8 tries to play it. Because RealPlayer 8 runs only in classic mode, your Mac attempts to switch to the previous OS.
To avoid this problem, remove RealPlayer 8 from your system. You may also want select Help > Check Default RealPlayer from the RealPlayer menus to ensure that RealPlayer 10 is your default player.