Do remember that if the Cations are of different charge the Ksp may be lying to you, but in the case where both ions are the same charge the Ksp values should tell which one precipitates first.
Ksp won't be lying, they just can't be simply compared then, but they still can be used to calculate precipitation order. And the problem is not in the cation charge, but in the salt stoichiometry, you can't directly compare CaCO3 and Ca3(PO4)2 even if the cation charge is identical.
Actually you kind of restated my point. I think you misunderstood me a little bit.
In a problem where you are adding a single anion to solution to separate two or more cations, the different cation charges will result in different stiochiometry coefficients and subsequently different exponents in the actual equilibrium problem. So yes the charge does matter when dealing with a single anion because the cations require different quantities of the anion to be eletroneutral.
It is a trap that gets many people who look at K
sp alone. While one K
sp may be smaller, when you actually do the calculations you end up taking the cube root or greater of the K
sp compared to the square root in a 1 to 1 cation to anion which results vastly different number.