Did some digging and it turns out, that’s kind of intended behavior. By default a sorting by task index is always pre-selected. This goes largely unseen but has a massive impact on sorting: All sorting columns are applied in the order of selection. Therefore, when you sort by due date while sorting by task index is enabled, it sorts by index first, and then due date. The index sort column takes precedence over the due date filter, making it pretty much obsolete.
Because this is confusing and doesn’t make much sense, I’ve changed this in 9cee720ac9 to makes sure the index sort column is always passed in last. Please test it on try in ~30 min.
I would like to handle the task sorting on the overview pages entirely on the server in the future which should fix these cross-browser issues with safari.