I have tested this extension on both a production wiki running mw:Header Tabs and a localhost wiki, and when both are enabled, any page with header tabs will not render properly, which results in the headers near the bottom of the page not rendering properly and the text being grossly enlarged.
I suspect the root cause is the fact that both extensions alter section behavior, and the corruption of the data results from MediaWiki trying to make both extensions work at the same time.
I'm not sure how this error could be resolved, but given it only affects pages with the headertabs parser hooks, I would suggest introducing a condition that disables SectionHide if the Header tabs parser hook is detected on the page.
Otherwise, it seems these two extensions are completely incompatible at present.