> I'm a fan of using painters tape.... pretty low profile, easily removed, stays on really well

The cleverest solution I've seen that is 1.) easily toggled, and 2.) harmless to screens is a coworker who built a little vinyl veil that attaches to the top back of their monitor. They can flip it forward to cover the camera, or flip it back to use it. But if you close even the tightest of lids with a couple microns of vinyl in there, it's harmless. Bada-bing, problem solved, and they only used a penny or two worth of materials.