There ARE exceptions to this basic rule. It all depends on the items each client has. You'll notice some clients' items, especially consistent clients (your weeklies and biweeklies), can be sorted to increase your efficiency and decrease the overall number of loads or time spent per client. The goal is to give each client's items as much care as possible without wasting time or energy.
Use your Judgment
In general, you want to stay true to form as much as possible, keeping in mind, as I have stated before, read the tags whenever you're unsure. For example, you'll note that not all whites can be washed with chlorine bleach.