What characters have been politically corrected before?
The question of Chinese minority nationalities' names is a bit more complex than that. Many of these minorities did not have a single, fixed name before they were catalogued in the 20th century. In fact, the definitive list of minorities was not fixed until the 70s. The Chinese writing system also underwent huge changes in the 20th century. 

Thus, many minority names could be spelled in a variety of ways, or the characters for them were not part of the Chinese standard in the first place. Under these circumstances, it's not surprising that the government would choose to write the names of minority groups with characters that had positive connotations. I assume the groups themselves also preferred a positive name. The description 


  the government changed some characters for the names of minority
  ethnic groups


is somewhat misleading.

That said, here are some examples:

苗 (Miao) could be spelled a number of ways, one of them being 猫
with the dog radical. Since this character already means "cat" and is then pronounced máo, reducing it to 苗, which means "young plant", is less confusing.

瑶 (Yao) used to be written as 猺, which also means "jackal". Again, changing the character is not only friendlier, but also less confusing.

羌 (Qiang) is a good example of a character that has always been written a variety of ways. One of them was 猐, again with the dog radical. I don't think it's too weird to choose a different spelling. 

Also, many Chinese minorities were called 蛮 (barbarians) in Chinese historical sources. One example is the 布依 (Buyi), who were referred to as 仲蛮 (Zhongman) in Qing dynasty texts. In such cases, it's not so much that the characters were changed, and more that the government began to use the name by which members of that group referred to their own group.

Ideology may have also played a small part in the way that Chinese characters were simplified into 简体字 (Jianti zi). I've always suspected that some Chinese anti-monarchist took some joy from replacing the character 後 (behind, after, later) with 后 (queen).

The character 他 was used as a third-person pronoun for both genders well into the 19th century. I assume this was split into 她/他 to conform to European languages. 

There is some movement in China to change the characters with negative meanings that have the "woman" radical. However, this is limited to a relatively small group, maybe comparable to the number of people who wish to use "xe" as a gender-neutral pronoun in English.