Answer
If the values of $\mu_1$ and $\mu_2$ are reduced, the least horizontal pull by the hands and push by the feet that will keep the climber stable will increase.
Work Step by Step
In order for the net horizontal forces on the climber to be zero, the hands and feet must exert the same magnitude of force $F$ on the rock.
Then the total friction force exerted upward on the climber must be equal in magnitude to the climber's weight.
We can find the minimum possible force $F$:
$F~\mu_1+F~\mu_2 = mg$
$F = \frac{mg}{\mu_1+\mu_2}$
If the values of $\mu_1$ and $\mu_2$ are reduced, then the value of $F$ increases.
That is, the least horizontal pull by the hands and push by the feet that will keep the climber stable will increase if the values of $\mu_1$ and $\mu_2$ are reduced.
