Just set YT's output to whatever the TV is using. You said "passive", but you didn't say what kind of passive. If it's interleaved, then set the output to interleaved. If it's checkerboard, set the output to checkerboard. And so on and so forth.
I'm using a Asus passive monitor, interleaved, and I just set YouTube to interleaved, and it works perfectly fine. Bear in mind that the resolution of your desktop must exactly match the physical resolution of your screen. That's what YT is using to generate the interleaved lines, so if your resolution is off, the lines that YT makes won't match the polarized lines of the monitor.
Welcome to Rivendell, Mister Anderson.