Time has come to move out of Hugo 0.34 to something never (0.128.0). Hugo is expanding quickly and unfortunately in backward incompatible way. Plus this site is already since some time on Github Actions not Wercker..
The easiest solution how to publish with Hugo to Github Pages is to have two separate repositories, one with blog source files and second with html files. Simple.
We can push files from both repositories manually or can do better. Push just source content and leave the rest for automatic deployment.
Update: Use Wercker. It is better.
While trying to make this little space in the web finally working, I set up dozens of different static site generators (Jekyll, Pelican, Nikola, Lektor, Sculpin..). I was even thinking about writing my own for some time. I tried wordpress and blogspot. But finally arrived at Hugo and it make my day much better.