The exact settings on your camera will depend on your model, but there's likely an auto option, a bunch of presets (daylight, cloudy, tungsten, etc.), and custom. Avoid auto white balance at all costs and opt for a preset or custom instead. If you have a top-of-the-line DSLR, there may also be an option to manually set the color temperature of the room, measured in Kelvin.
Turns out, the webinar had already been recorded, and wasn’t “live” at all. It was deceptively designed to appear that way — my own comments were inserted into the “chat” stream, but no one saw them except me. Every other comment in the chat was canned, along with Neil’s presentation. They tried to cover this by having the “technical” guy say “If I don’t get to your question, email me” in the chat stream.