Should moderately soluble compounds like calcium hydroxide be denoted (aq) or (s)?
In principle, you cannot know without conducting the experiment. It depends on the concentration of a moderately soluble compound such as $\ce{Ca(OH)2}$ whether it is dissolved or whether there is stuff still sitting at the bottom of the vessel undissolved.

However, you are performing a reaction which is in aqueous solution. This reaction will typically only work if all the reactants are already in solution. Moreover, this is a precipitation reaction. Thus, it wouldn’t make sense to have a non-dissolved reactant to react it with a dissolved one. Given this context, you should assume both reactants are in solution.

$$\ce{Al2(SO4)3 (aq) + 3Ca(OH)2 (aq) -&gt; 3CaSO4 v (s) + 2 Al(OH)3}$$

Note that whether or not aluminium hydroxide precipitates depends on the resulting $\mathrm{pH}$ value. If you started off with excess hydroxide, it may well stay in solution.

The exact answer for a given compound can only be known if you know both concentration and solubility product.