How much of our impression of mathematics as a creepy, mental-health-harming cult

Er, what? Who do you mean by "we"?

comes from pure stereotyping?

The link says of Turing:

Finally, Alan Turing, the great Bletchley Park code breaker, father of computer science and homosexual, died trying to prove that some things are fundamentally unprovable.

This is a staggeringly wrong account of how he died.