When is it reasonable to ignore channel length modulation in MOSFETs?
Obviously for any circuit in which the drain-source impedance of the FET is not an important parameter. 

It clearly depends on the circuit and biasing conditions, but that mostly only leaves source followers and many switching applications. 

The approach I generally follow is to ignore it unless it’s patently obvious that it matters, and calculate it after the fact to check how it compares to the node impedance. This does mean that in some cases you would have to solve the circuit twice, but in real designs by hand it might simply require an approximate correction. 

Ignore but verify. 

In most cases, hand calculations only provide a ballpark figure anyway. Its value lies in providing insight and intuition into the effect of the different circuit elements.