What is this obsession with legitimacy?
No, you don't give them legitimacy if you bring them up on a stage, debate them, and prove them to be 100% wrong to the audience. Again, with the two examples I mentioned, it would be exceptionally easy to defeat in a debate, thus proving them wrong.
- - - Updated - - -
But we both know both flat earthers are an extreme minority and anti-vaxxers are a losing battle right? Because both get debated and defeated over and over.
Why not let them continue to lose?
You will never fully 100% eliminate a belief. But defeating it enough time and it's pushed out of common thought of society.