tabs don’t work with SO or even Jetpack contact form

This is a limitation of the tab depending on how the data inside the same is processed. The tabs other than the first one are hidden (display: none) when the page loads and hence not available for processing. Only way is to move them outside of the tabs.

By the time they get displayed by user clicks, its too late since the processor is already done with processing and cannot be invoked again since we do not know before hand what goes inside them.