The hidden purpose behind these changes in language is to make it so that a person being forced, perhaps, to give preferred pronouns who then chooses "she, her" is automatically assumed to identify with femininity, not with her actual biological sex.
The former identification is likely to enforce sexist stereotypes about what being a woman means, the latter simply states one mostly observable fact (that she is biologically female) and tells most of us (except for extreme patriarchal religions or anti-feminist groups) nothing about that person's abilities, basic character, or preferences. So the latter makes the liberation of women feasible, the former pretty much closes us out of that option.
When 'they' is added to the list of pronouns, what is also added is the idea that only 'they' are not strongly clinging to traditional sex stereotypes and traditional gender roles for women and men. This is very bad for feminism, women's rights, and, as is evident in another recent thread here, even the history of female role models now often posthumously transed.
All this is the hidden underbelly of the gender identity ideology. It is built on exactly the same rigid sex/gender roles as extreme patriarchal views, with the one exception that some are allowed to jump from one box to another, in theory, but in practice women can only do this by modifying their bodies and by taking hormones.
The nonbinary option only works as long as most women accept being called women, because female people identifying as nonbinary only do that in relation to the vast numbers of women who are not (yet) doing that.