Each profile field has a setting called Offer this field as a filter on the Students screen and in exports. It’s off by default.
Turn it on for the few fields you actually filter by, like an organization or a region. The Students filter bar, and the export panel in Pro, gain a filter for that field. Leave it off for everything else and those screens stay tidy.
To turn it on, go to Settings, then Profile Fields, edit the field, and tick the box.
A known limit with Other answers
The filter dropdown lists the choices you defined. Answers people typed under Other don’t appear in the dropdown, but they do show on the Students screen and in the CSV export.