It looks like the default warning-face is getting overwritten.  When I
run `emacs -Q` and then `M-x customize`, warning-face is DarkOrange, as
expected.  But when I run emacs with my init file, it’s set to Red.

Is that the same as what you’re experiencing?

For me the culprit was the Solarized theme, which themes the
warning-face: https://github.com/sellout/emacs-color-theme-solarized/blob/master/solarized-definitions.el#L236