The browser version of AirTable has “TODAY” as an option. To cancel, you just click away from the dialog. The mobile version has three buttons: “CLEAR CANCEL OK”. It cancels anyway if you tap out of the dialog, so a cancel command is not really necessary. So, why not replace the CANCEL option which is not in the browser version anyway, and have the mobile app date picker have the TODAY button? This will make the two versions behave in the same manner.
This at first glance would be an easy fix.