Rules as written, Tumbling Fool completely undoes the effects of Equine Build, so you climb at the same speed you travel by foot (or hoof I guess). Equine Build is modifying a general rule for how you use your normal (non-climbing) speed to climb when you don't have a climbing speed; Tumbling Fool gives you a climbing speed, so the rules for climbing without a climbing speed no longer apply, and therefore neither does Equine Build.
It would be entirely reasonable for a DM to say "Nope, that's complete nonsense" and house rule things (e.g. they might split the difference and have you effectively have a climbing speed of half or a third or a quarter of your speed, any of which would still be better than one fifth of your speed), but it's a very clear interaction as written; when they don't have a climbing speed, centaurs are bad at climbing, but if they gain a climbing speed by any means, they're as good as anyone else with that climbing speed.