I see this claim quite a lot, and I think this is vastly exaggerated. I've just looked at the signings of last decades, and Bayern tends to buy mostly internationally or from lower tier clubs. Not from their actual rivals. The only signings that would fit that description in the past decade would be Mats Hummels (a player they sold back to Dortmund after one contract term), Mario Götze (also sold back after one term) and Lewandowski. So there's one signing that actually lasted at Bayern where I would agree with you that they "took a player from their strongest rival". However, as can be seen every week, for a good reason. Not to hurt Dortmund as much as getting themselves arguably an European top 5 striker.
In addition, Hummels is still performing just fine for Dortmund and Götze, well... one hit wonders do be like that. So, to be frank, I have no clue what you're on about. But looking at the entire transfer volume for Bayern, they get more of their own youths into the first team than "taking players from their strongest rival". And let's be clear on this, "the strongest rivals" for Bayern don't play in the Bundesliga. They play in other leagues and have names like Barcelona, Madrid (either one, tbh), Juventus, Liverpool etc.