There are likely a few worthwhile Jekyll plugins, but I’ll let someone else chime-in for recommendations as I’m not too familiar with that side of the plugin world.
One option might be DataTable, a jQuery plugin for manipulating HTML tables. I’ve had good success using Jekyll to transform data into a basic HTML table (a simple Liquid loop), and then use DataTable to add search/sort/filter functions.
For the type of filtering you want, the closest example-code might be the Multi-filter:
I have done something similar with ThemeJekyll (click the filter button on the left), but I only used Jekyll to generate JSON and then used Vue.js to do the filtering and rendering part. Doing it this way does require a good bit of JavaScript and Vue knowledge, but it works nicely and isn’t dependent on a third-party service.