The two museums were the Museo Soumaya which I have visited before and the Frida Kahlo Museum, which I have not. The ideology of each is quite clear and there is really nothing mysterious about it. But oddly enough, I suspect most visitors are oblivious to it. Here is my take on each.
The Museo Soumaya, Carlos Slim's tribute to his wife, is a wonderful triumph of architecture and presentation. The building is very modern and innovative and the contents are presented with clarity and professionalism. (The top floor remains devoted to an exhibit of sculpture, mostly Rodin and Salvadore Dali and the rest is a selection of artworks of various kinds from the 17th century to the present.) Not surprisingly, given that it was the creation of the head of a wide range of companies that include communications and technology, the ideology is simply that the important values to hold are modern and technocratic ones. Let me emphasize that there is nothing wrong with this. Mr. Slim has every right to promote those values he believes important. Perhaps people miss the ideology because it is so simple and straightforward.
UPDATE: Here is a photo I took of one of the Rodin sculptures in the exhibit:
The Frida Kahlo Museum has quite a different ideology. For one thing, since it was her home, it has the feeling of a shrine as her bedroom(s) and kitchen are faithfully preserved. It is this very preservation that gives us the ideological clue. In one of her bedrooms are displayed photos of several people she particularly admired. They include Leon Trotsky, who resided with Frida Kahlo for a while and whose bedroom is also preserved in the museum, Karl Marx, Vladimir Lenin, Joseph Stalin, Mao Zedong and someone I didn't recognize (maybe Engels?). There is quite a lot of recent scholarship that attributes an astonishing toll of deaths to these figures (well, maybe not Trotsky and Marx). You might call them the greatest mass-murderers of the 20th century, which would come as a bit of a surprise to Hitler, I'm sure. A more palatable aspect of Kahlo's ideology in the museum is her collection of folk-art, showing her connection to the people.
Now, how am I going to tie this to music? A lot of recent musicological scholarship has tried to uncover the secret ideological subtext to a lot of music. Sometimes, as when it was discovered that the CIA had a program that supported the work of the post-WWII serialists in Europe, this has proved to be a bit uncomfortable! But in other cases it has proven quite interesting. Richard Taruskin has published innumerable essays on the ideological content and origins of the neo-classical and early music movements. Turns out they both originated in the Stravinsky circle.
But here is my point, and I actually have two. First, there is quite a lot of music that does have some or a lot of ideological content. There is no denying that the glories of the French Baroque in the operas of Rameau and the instrumental music of Couperin, were intended to gild the Bourbon lily of the French royalty (the very title of some of Couperin's pieces, the Concerts royaux shows that pretty clearly). But that brings me to my second point, in order to be truly effective, this ideological content needs to be pretty obvious. There is nothing subtle about one of the prime and original examples of musical ideology, the Marseillaise of revolutionary France. It was originally titled "War Song for the Army of the Rhine."
But a very subtle and covert ideology is really a contradiction in terms. It just won't fulfill an ideological function. Have a look at the examples of Socialist Realism by Shostakovich. The subtle, covert aspect is what musically contradicts the overt message!
So the conclusion is, yes, some music has ideological content, but it is usually poorer for that. The best music very much transcends the ideology and historic and social content of the time of its composition and this is as true of a Shostakovich symphony as it is of a Beethoven string quartet or a harpsichord piece by François Couperin. Speaking of which, let's end with one of those. Here is (are?) Les langueurs tendres from the Second Book: