Hydrostatic equilibrium yes, but equal? No. We agree that centrifugal force is a factor. Now ask yourself, why would gravity suddenly strengthen at the equator to get the surface acceleration to stay equal to that of the poles?

It doesn't. As a result the Earth seeks a new hydrostatic equilibrium, bulging out at the equator. This in turn strengthens the centrifugal force a bit while also slightly diminishing the force of gravity (because more of the planet's mass is farther away). So the same effect is taken even further. Local differences add a layer of noise on top of this, but the end result is that the net surface acceleration is measured to average slightly less at equatorial regions than at the poles, with for example Singapore getting 9.7639 m/s2 of downward acceleration, while Helsinki gets 9.825 m/s2.