I strongly suspect that people who make the claim "no amount of evidence could convince me of not-X" have simply absorbed the meme that X must be supported as much as possible and not the meme that all beliefs should be subject to updating. I very much doubt that expressing the above claim is much evidence that the claim is true. And it's hard to absorb memes like "all beliefs should be subject to updating" if you are made to feel unwelcome in the communities where those memes are common.