No wonder many Thai people hate this movie
When Anna replaces the old Siamese map with the new English one, she replaces the local and implicitly inferior knowledge of the Siamese with a metropolitan and implicitly superior knowledge derived from European models. In the best Orientalist fashion, she denies the Siamese the ability to represent themselves and insists that they can only truly know themselves through a Western and literally Eurocentric system of knowledge.
True, the movie does point to how the differences among people can be transcended, the kinds of bonds that can be forged, and the nature of communities that can be created. However, the relationship between East and West is very asymmetrical. For example, after Anna teaches the children her dance, the children teach her a fan dance, so she can understand their culture as well. The equality of the exchange, however, is deceptive. The goal of the scene is to change the Siamese, not her.
Thai anger at this condescension goes all the way back to the publication of the original source, Anna Leonowens' memoirs published in the 1870s. The Thai elite were offended (none but the elite had access to the memoirs) and the government apparently tried to buy up the whole edition of the English Governess... to prevent its distribution. When Margaret Landon turned Leonowens' exploits into a best-selling novel, Thai offense turned to outrage. The King and I only worsened matters and the government banned the musical as an insult to the monarchy. Visitors to Bangkok in the 1950s were warned not to mention Anna and the King to Thai people, who were insulted that the story distorted history by giving credit for Thailand's modernization to a relatively minor - and Western - employee of the court.