You can’t reason someone out of an unreasonable position.

Hitting a flat earther with logic and facts will obviously be counter productive. Even a modicum of empathy and curiosity as to why someone thinks the way they do will serve you well.

But in that case, the battle is already lost. I cannot engage with the person in a manipulative emotional way to use their emotions to shock them out of their mistaken positions. Any further communication regarding the matter is useless. And glossing over some topics is being an accomplice, but apparently that’s the only viable response.

Conversations are about much more than who is wrong and who is right.

Departing with people espousing damaging views for society, given that as you say reason is not a tool that works, is pointless.