My previous solution has the unwanted effect that it overwrites already set dates that are in the past to the current day.
Correct solution came from https://stackoverflow.com/questions/62204645/disable-dates-and-days-of-the-week-in-acf-date-picker
acf.add_filter('date_picker_args', function( args, $field ){
args['minDate'] = '0';
return args;
});
For other users looking for this answer, the current syntax is a bit different:
// Don't allow picking dates in the future
acf.addAction('date_picker_init', function( $input, args, field ){
$input.datepicker('option', 'maxDate', 0);
});