Dishwasher Air gap

Is an Airgap required in all states? I ask because it seems its impossible to install one without going through different adapters to fit the hoses. Installed a NEW dishwasher with its own hose which won’t fit onto correct port on NEW Airgap. Hose was 3/4" but port was 5/8". Outlet end of airgap is 3/4" and required another hose to go to the disposer - also with 3/4" port.
Why the different port sizes on the airgap?
If I avoided the airgap altogether the new hose from the new dishwasher would have fit perfectly on the disposer. Huh?

Just need a quick trip to Home Depot. How are they to make money if everything is too easy? :shock: