You may be right that it is common to dismiss arguments that invoke Gödel's theorem. I've been guilty of this myself. However, just like with quantum mechanics the reason is that there are just so many people who invoke Gödel's theorem without understanding it as a technical result.

I'm not talking about "pseudointellectuals" in this case, unlike with quantum mechanics. I'm talking about actual working mathematicians who use oblique references to Gödel to, e.g., dismiss formal methods or constructive logic as worthless.

This is extremely annoying, since Gödel's theorem's, as the article rightfully points out, are precise statements about formal systems. There's nothing mysterious about any of it. When someone invokes Gödel you can usually take it to mean "I don't want to engage with this topic further" and not as a serious argument.

> This is the man who "proved" God's existence with modal logic,

I'm pretty sure that was a joke. The final assumption he makes in this proof is logically equivalent to "god exists".