Yes , the law of conservation of mass obeyed in net ionic reactions.
Net ionic equation shows only the chemical species that are involved in a reaction, it doesn't include spectator ions unlike a complete chemical reaction that involved spectator ions too.
Example of a net ionic equation:
It can be seen in the image attached.
As it can be seen from the net ionic equation that the mass of reactant equals to the mass of product , so law of conservation of mass is obeyed in this .
