I've seen math / physics majors make an easy transition into software development. I bet that is much easier to pull off than switching to programming from say, sociology.
Sociology curricula are getting quite quantitative these days — the jump from sociology student to data scientist isn’t that far. I used to live with a bunch of sociologists back in grad school, and they lived and breathed R, Python, and SAS.
I have a physics degree, and while I'm not employed as a programmer per se, programming is my main problem solving tool. It wouldn't be a quantum leap for me to move into a programming job if I wanted to do it.
On the other hand, I also have two friends whose college degrees were in philosophy and music performance, and both became programmers.
Do employers in some parts really salivate over green math/phys grads with not so much as a github profile? Or do these anecdata leave off some key arc to the story where the grad does something substantial to bridge the gap between said major and software dev?