I think the Stuttgart match to be played in Munich Arena will end with Bayern Munich's victory. Because Bayern Munich does not lose easily in their own field. Also, their situation this year is better than last year. However, I agree with you that they conceded too many goals. The technical director has probably identified the deficiencies since he was a player in the defense zone when he was a football player in the past. He will definitely request transfers to those areas during the mid-season transfer period.
The difference between playing at home and away is that you have the support of more fans on your home ground. They have not lost any game at home this season, but from the three recent games they have played, Bayern is not reliable. They drew against Eintracht Frankfurt and Bayer Leverkusen and lost against Aston Villa. I would bet on them to win the game but I would not place it with much money. I just hope coach Vincent Kompany fixes this team because Bayern is not a patient club. Getting new players in the January window is important but for me, the club has enough quality to get good results.