Can we split solid ionic compounds into their constituent ions when writing an ionic equation?

The equation for the reaction between magnesium and copper(II) oxide is:
$$\ce{Mg + CuO -> MgO + Cu}$$
Here, we can write the net ionic equation as:
$$\ce{Mg + Cu^{2+} -> Mg^{2+} + Cu}$$
The $\ce{CuO}$ here is a solid, so why can we still separate it into its constituent ions?
In a neutralization reaction, if the base is a solid then we cannot split it into its constituent ions (as far as I know). For example, the net ionic equation for the reaction between copper(II) oxide and sulfuric acid is:
$$\ce{CuO + 2H+ -> Cu^{2+} + H2O}$$
So why are the rules different in the two reactions? Why can we split the $\ce{CuO}$ into its constituent ions in one reaction but not the other?


