According to the official site, Oktoberfest this year starts on September 19, so the 10th shouldn't be a problem.
On the 1st, you'll go through outgoing passport check, emigration, but I doubt that there will be that many people leaving just before the last weekend.
The only place I can foresee a problem would be with the shuttle if you arrive at the new satellite terminal and depart from a gate in the main building.
This is probably only ancient history since it was almost 20 years ago, but in 2007 I arrived at MUC on the last Thursday of Oktoberfest, as you will be doing, and I don't recall the airport being unusually busy. In fact, even the Hbf was not that busy. It was just that the street from the Hbf to Theresienwiese was an "ant trail" of people going to the Oktoberfest grounds.
But, then, that was almost twenty years ago.