Solubility for hydrated calcium sulfate in HCl

[Kruz87]

was asked to consider the solubility for hydrated calcium sulfate in HCl.
The principal acid my proffesor had posted for the solution was [ CaSO4(hyrdrated) + HCl <--> H30^+ + Ca^2+ + SO4^2- ]. I guess what I'm asking is what happened to the Cl^- and why isn't it reacting with Ca^2+ to produce CaCl2. ? It's not a spectator ion right? But if it is why?

 

[symbolipoint]

Chlorides are soluble, and the chloride ion will remain freely ionized. The "calcium chloride" will be present as ions of Ca(+2) and Cl(-1)