You can only ignore that term when you ignore loss.  This is actually pretty common practice in simulations.  In the frequency-domain, the J term is usually incorporated into the permittivity so you end up with a complex permittivity when there is loss and no J term.  Technically this is not ignoring the J term.

Dr Rumpf rightly said. When you consider loss less media or Ideal condition

This equation tells us that the magnetic field is originated by currents. There are two types of currents, the displacement current dD/dt which exists whenever there is a rate of change of the displacement with time, and the current J due to the movement of the free charges in the medium. J=qnv where n the free charge density and v the velocity of these charges. J in this form, is termed the convection current. The convection current has two forms, the diffusion current and the drift current.The driving force of the drift current is the electric field where the driving force for the diffusion current is the concentration gradients of the mobile charge carriers. So, when ever free moving charges are existing in an an electric field, a current J will exist. So, for J=0 , n=0. That is the medium is free of mobile charges.

This may be a basic insight.

best wishes.

However, adding to the above answers, if there is an impressed external current source (current not due to the conductivity or resisitivity of the medium but an externally added source) , and we want to find the electromagnetic characteristics due to that source, we can't neglect J.. Here by J ,I mean an external impressed current source.. To summarize, we can neglect J  ( J is J-losses + J-impressed) completely in a source-free lossless medium.