And really it's not an issue with Netflix as much as with Windows Media Player. WMP 11 works fine on a standard Windows XP installation, and even on Media Center Editions from 2005 on. But if you bought into the Microsoft HTPC technology before it reached its fourth generation you're out of luck unless you want to use a hack that will cause the Media Center application to stop working.
At this time the only workarounds for the problem are either upgrading your version of Windows MCE or changing HTPC software. Unfortunately, dropping MCE also requires that you replace your remote as well since no other software is capable of communicating with a MCE remote.
If you're considering a change to keep streaming from Netflix there may not be any good solutions. If you upgrade to a newer version of Windows MCE you're essentially paying Microsoft to fix the problem they caused in the first place, and it will probably cost you a minimum of around $200.
If you go with different HTPC software, such as BeyondTV or SageTV, or even a free option like MythTV, you'll need a new remote, or at least a new sensor for the computer to receive signals from the remote. In addition you may also need to buy a regular copy of Windows XP, or at least learn to hack the version you have to get around Media Center's limitations.
We'll make sure to keep you updated with any new developments - hopefully including a response from Netflix.