In uniform circular motion, the acceleration is perpendicular to the velocity at every instant. Is this true when the motion is not uniform-that is, when the speed is not constant?

No.

Explanation:

Through uniform We can presume you mean constant in both that is in magnitude as well as in direction ⠀

When you apply a steady, non-zero acceleration to a resting body, the velocity can be parallel to the acceleration and not always perpendicular at any time later.

We can do the same for an object with an initial velocity in a direction which is different than that of acceleration, and the direction of its velocity will asymptotically approach to that of acceleration over time.

In both cases the motion of a object undergoing a non-zero persistent acceleration can not be uniform That is the concept of acceleration: the velocity change over time.