Hi, aab1. I usually cut 24-72 hours later. It can depend on the recipe how quickly the soap gets hard enough to cut, but that timeframe generally works for me. Like you mentioned, some soaps need to be cut sooner, like salt bars. I've seen folks at farmer's markets cutting bars off of what I assume is a cured loaf.
I touch a corner of the surface to see how the soap is doing before cutting. If it feels firm, I cut; if it still seems soft, I'll wait another day or two.
I almost always gel my soaps, too, which can make it easier to cut sooner. Ungelled soaps can be a bit crumbly if they are cut too soon, so I'd give ungelled soaps a little extra time.