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Airtable forms cannot enforce this with a date field. One alternative is to used a linked record field to a table of dates. You would have to create all the dates in advance, then add a filtered view to only show dates at least 3 business days in the future. You would probably need a formula field to calculate how many business days each date is from the current date. Then in the form limit record selection to the filtered view. Your users would loose the calendar picker and have to use a drop-down record picker instead.
Or you can go with a third party form system that has advanced data validation features.