Climbing and difficult terrain are two different things.
I think the root of this question is nothing to do with either centaurs or rangers, but a fundamental misunderstanding regarding the climb mechanic in D&D 5e.
As the basic rules go, climbing costs 1 extra foot of movement for each foot moved. Difficult terrain also costs 1 extra foot of movement of each foot moved. But climbing is not difficult terrain; they just have similar mechanical effects.
An ability that allows you to ignore difficult terrain, such as Land's Stride, does not allow you to ignore the extra movement cost of climbing or swimming. Similarly, climb or swim speeds let you ignore the extra movement cost for those kinds of movement, but don't let you ignore difficult terrain. So a DM could decide that climbing a crumbly cliff face counts as moving through difficult terrain, and thus costs triple to move across (unless you have a climb speed, or a way to ignore difficult terrain, or both, each of which would reduce the cost by 1).
So Land's Stride doesn't negate the Centaur's unique difficulty with climbing, because Land's Stride wasn't helping with climbing in the first place. They're just two different things.