I was just looking at the waste pipe install my plumber did. It is 1-1/2" ABS with P-trap serving both a carbon filter and softener tank that are timed not to overlap. It does not have an air gap.

I have observed them in operation. At the end of the drain cycle the clear hoses to the valves quickly fill with air, leading me to believe the valve does not allow a cross-contamination situation to occur.

Is this an OK situation or should I install an air gap just so a theoretical building inspector will pat me on the back and tell me I did the right thing, even though it is safe as-is? No, I'm not going to get this inspected.