Why are high values of capacitance in low pass active filters not recommended?
High values of C would imply low values of R, therefore high signal currents. 

In simple circuits (e.g. emitter followers) when the signal current is a large proportion of the quiescent current, you have to consider the device's nonlinearity (i.e. distortion). In op-amp based circuits, as long as the opamp has sufficient bandwidth and drive capability, this is a lesser concern.

In either case, high signal current means high supply current, i.e. heat and wasted power.

However, go too far in the other direction, and low signal currents mean high resistor values, and higher noise (both shot noise from the lower currents, and Johnson noise from the higher resistances). 

The right balance depends on the application.