Answer
See work.
Work Step by Step
The grip feels secure because the coefficient of static friction is large enough in this situation. Also, no horizontal forces are required to keep you in equilibrium.
However, if you move your bare feet relative to the wet bathtub, the smaller coefficient of kinetic friction is applicable, and a horizontal force may be required to regain your balance. You may not be able to compensate using the smaller frictional force.
