It's actually a very weird situation. Not only was Landauer one of the most important presidents of the club, he was also jewish. After fleeing from the Nazis, he returned to the club after the war. FC Bayern was friendly towards jewish people, incl. players, while 1860 was the "german" club. Yet they so rarely talk about that. A friend of mine works as a tv-journalist and did a piece about both clubs during the Nazi regime, but the Bayern management was extremely uncooperative and wouldn't give him interviews etc.. Rumor has it that the club doesn't want to blow that trumpet too hard because it might spoil their marketing prospects in islamic countries (e.g. the emirates)... what a world.
I wouldn't put such motives beyond them, but it might also be (or have been) a -possibly smart- policy of not stressing the jewish heritage as to not give idiots a front to attack.
In fact, as you say, FCB has a strong jewish heritage - but never was explicitly "jewish" in culture. BM was founded by intellectuals and students at home in the Schwabing bohéme, and as such it also attracted jewish people, but if you want to label it, it would more be
cosmopolitic. The opposite of the typical working-class neighborhood club. Also Landauer was jewish, but also almost a role model of the typical
Münchner of that era.
Also the club wasn't exactly a center of the virtually non-existing opposition against Hitler, as some may think now. They pretty much followed suit with every other sports club after Hitler came to power, expelling jewish members etc. Nevertheless they were target of certain repressions, the Nazis obviously didn't love clubs with such roots, while others, like 1860, were supported and favoured by the regime.
Truth is that for decades the club acted as if it didn't exist before 1963 - not entirely uncommon in Germany in the 60ies and 70ies
. And, unfortunately, thought for some period it should be the archetypical provincial "bavarian" club, including team photo shootings in Lederhosen, a mascot called "Bazi" and other such horrors. They seem to find a better path at the moment.