I was listening to a podcast once, and the host articulated something profound in a very well-stated way. He said (I paraphrase):
"I will never argue with a flat-earther, or an anti-vaxxer, or any of those people. The reason is because that these people have made that into _their whole identity_, and they are prepared to address any possible argument I could come up with. And because I care about facts and truth and they do not, my only possible response would be '...uh, I'll have to look into that, I don't know off the top of my head'. It doesn't matter that their response is incorrect or based on faulty research or has been rejected by the scientific community or whatever; by the time I discover that, they will be long gone and talking about how they won another debate."
This is it in a nutshell. If you argue about an issue with someone who has made _that one issue_ into the core of their persona, you will lose unless you are someone who has made arguing against that issue also into the core of your persona.
Of course I know that Andrew Wakefield is a liar and a scammer and of course I know that Apollo astronauts placed retroreflectors on the Moon which can be used to prove that they went there and that their photos of the spherical Earth are real, because I've done enough research to convince myself. But have I done enough research to convince someone who refuses to be convinced? And someone who has also done that research and come up with plausible-sounding nonsense to counter each of these arguments? Why would I waste my life doing this?