Well, from what I've read few years ago the chairman of Adidas serves also as the chairman of Bayern. But, of course, the football operations are delegated to people linked to the club. I believe that's Oliver Kahn currently.
But again, Adidas/Audi/Allianz are all local Munich brands.
Oliver Kahn was fired over 2 years ago actually. Bayern is lead by the president Herbert Hainer (former CEO of adidas) and sportsdirector Max Eberl. The President is elected by the General Assembly of its members. Because they are a joint-stock company, they also have a supervisory board with 9 members. Hoeneß and Rummennige are included there. And then some other CEOs whose companies have bought Bayern stocks.
If Bayern wants to buy a player, they have a magical 50m treshhold. Everything under it Hainer and Eberl can decide together with the coach to buy the player or not. 50m and above transfer needs clearence from the supervisory board first.
That's more or less how they operate. In reality Hoeneß still leads the club behind the scene, as especially Hainer keeps listening to him. Wirtz and Woltemade were his personal targets and he didn't get neither.
PS: They're Bayern brands, not actually München. Audi is from Ingolstadt, Adidas from Herzogenaurach. BMW is a Munich brand and there were some talks that they wanted to take over from Audi, but I don't know what happened to it.