First things first, this problem is already described and acknowleged as a bug on Github.
If FPC (varnish) is enabled, the
active HTML class will be missing from the category menu on the frontend. None of the usual things helps including
rm -rf pub/static/*, redeploying static, reindexing or flushing caches.
Though the currently active category receives the proper HTML class if you disable FPC.
Since this problem is known but the Magento team seemingly not interested in fixing it. I'd like to know if anyone has found a way around this behavior - neither disabling the cache nor having no visual clue of the current category is desirable.