I would suspect that Clancy probably does recieve some money for product placements in his book. And I dont think that this is a rare occurence in any form of media.
Except for the John Hopkins example. The main characters in those books either went to school, or taught or practice medicine at John Hopkins. These are the same characters he has been writing about for years, so I dont really think that this is a form of product placement, rather I just think it is a part of the story.
I'm also not sure that the racism and misogyny that you discussed are as big of a problem as you make it out to be. When he writes these things, these are the thoughts, words and actions of characters in the book. This is a fictional story, and like many other fictional stories, some of the characters are not perfect people. Now it's certianly possible that some of Clancy's personal views may be seeping into his characters, but that is not a big deal IMO, I never noticed these traits to be uncharacteristic of his fictional characters.
I also think that it is possible that Clancy is merely writing what he sees. The vast majority of the leaders of this country are WASPs. And it would not surprise me at all to find out that some of these people are racist or sexist.
I think on the whole, Clancy's books are not nearly as good as they used to be. I havent yet read 'Red Rabbit' but I did enjoy ' Bear and the Dragon' however, I dont think it is on the same level of some of his early books. It all seems pretty by the numbers now.