I'm beginning to lose confidence in our fan base knowledge. Again, not a single correct answer. So let's look at these series.
These 5 series have played a total of 285 games in consecutive seasons.
Florida St and Miami have played the fewest total times of the 5 listed, having met 46 times since first meeting in 1951. But they’ve played consecutive seasons for only the last 46 years.
Pitt and Syracuse have met 70 times, the last 60 of which have been in consecutive seasons.
Clemson and Wake Forest have played 80 total games. They began the series in 1933, and have missed just 2 seasons in that time. After their 1st game in 1933, they skipped 1934. The only other season they missed was the year before the ACC was formed, 1952. Since then, they have played every year that the league has been in existence, 62 years. But wait! This series doesn’t count. Both of these teams were charter members and don’t meet the question criteria that at least one team WAS NOT a charter member of the ACC.
Duke and Georgia Tech first played in 1933, 82 seasons ago. Interestingly, they are the only team in this group that have played every year since their first meeting. So they have racked up 82 consecutive seasons of contests.
The oldest of these series, however is Virginia vs Virginia Tech. They have played both the most games, 96, and the earliest that any of these teams have met, 1895. They’ve played 87 of those games since 1933. But that was 92 years ago. In the War years of 1943 and 1944, Virginia Tech did not field a team. The war effort probably sapped up all the technical personnel available, including a significant portion of bodies that might have played football! Thanks for your service Hokie nation, but couldn’t you at least run some 4F’s out there just to keep the series alive! Well, it didn’t matter anyway, as they also skipped 3 years from 1966 to 1970. Since then, they’ve played 45 consecutive seasons.
So the answer, with 82 consecutive seasons played, longer than all but 3 other consecutive series between ACC teams (Duke vs North Carolina 93, Virginia North Carolina 96, Wake Forest vs NC St. 105) is Duke vs Georgia Tech.