Figured it out.
First: the certificate for meta.apple.stackexchange.com is definitely invalid. That is, ultimately, at the heart of my problem.
But the problem for me, in Chrome, was caused by my use of the HTTPS Everywhere Chrome extension. It was responsible for blocking the http calls to meta endpoints that were being made from an https meta page. Once I disable the extension for meta I could vote again.
This all, however, is just pointing a serious flaw in the use of https on the meta sites that needs to be fixed. I'll argue this stands as a bug.