The quick answer to that question in the title is...the same as it affects everyone else. But let's run through the specific changes and see what they mean.
1) Teams from the same conference will no longer be required to wait until the Elite 8 to play if eight or fewer teams from the conference reached the tournament. The new rules:
Conference foes that played once during the regular season can face-off in the Round of 32. Teams that played twice during the year can play each other in the Sweet 16. If teams played three times during the season — a home-and-home during the regular season and a matchup in their conference tournament — they will have to wait until the Elite 8 to play.
2) The top four teams from a given conference will be placed in separate regions only if they are all to four seeds. Previously, the top three teams from a given conference had to be in different regions regardless of where they were to be seeded.
Syracuse Orange fans are no strangers to early-round match-ups with conference foes. We met the Marquette Golden Eagles in the Round of 32 a couple years back (a game which may have never actually happened...). At the time, it sucked. Obviously because we lost, but also because it seemed like a conveniently-shady way for the NCAA Tournament to get rid of Big East schools by pitting them against one another early.
Of course, because the rules are only in effect if a conference has eight or less teams, and you can probably expect the ACC to challenge for 8-10 NCAA Tourney spots on a regular basis, these rules might not even come into play. Which means the chances of seeing North Carolina or Georgia Tech in the Round of 32 remain a possibility (The chances of seeing Pitt and Notre Dame in the Round of 32 are decidely-less likely because they're Pitt and Notre Dame).
All of that said, I like anything that separates out conference schools to make it as hard as possible for them to meet in early rounds.