How does the Athlete feat affect the Centaur playable race?

Question

The Athlete feat (PHB, p. 165) has a point that says:

climbing doesn't halve your speed.

The Centaur's Equine Build trait (GGtR, p. 16) says:

any climb that uses both hands and feet is especially difficult for you because of your equine legs. When you make such a climb, each foot of movement costs you 4 extra feet, instead of the normal 1 extra foot.

The normal climb normally costs half your speed and athlete negates that, but the equine build costs you 80% of your speed instead of 50%. How would these two interact with each other?

This question has nothing to do with the difference between listed climb speed and walking speed.

Answer 1

As of the 2018 Errata, the Athlete feat has been changed

Athlete (p. 165). The third benefit should instead say climbing doesn't cost you extra movement.

—Errata: Player's Handbook, 2018

Because of this change, the Athlete feat would allow a Centaur to ignore all extra costs associated with climbing. The technicality of ignoring "halved" movement speed is no longer relevant.

Answer 2

You become a mountain goat and essentially have the best climbing in the natural world.

Athlete (p. 165). The third benefit should instead say climbing doesn't cost you extra movement.
~ 2018 PHB Errata