Not always, for example, Native American on reservations use the term Indian to refer to themselves, but outside this is becoming impolite in favour of Native American (including among some but not all Native Americans)[1][2]

See also the "Spastics Society", "National Association for the Advancement of Colored People", modern use of the n-word among black people, the use of "Negro" in "I have a Dream". Plenty of cases where a word in use by the group themselves becomes considered the impolite word.

[1]: https://www.youtube.com/watch?v=kh88fVP2FWQ

[2]: https://en.wikipedia.org/wiki/Native_American_name_controver...

"colored people" is a wonderful illustration of this farce because NAACP kept the name so long that it went from preferred to offensive and almost back to preferred, with "people of color" being the PC term in US (and "people with Foo" becoming dispreferred to "Fooed people" or "Fooed"/"Foo", and "racialized" being the PC term in Canada (which would be horrifically offensive in the US).

I enjoyed the suggestion I found somewhere that the NAACP should replace the problematic term "Colored People" in its name with "African Americans".

What happens if the name you chose for yourself doesn't match the name a Twitter mob chose for you, and they attack people using the name you prefer?

Approximately 97% of "Latinx" people do not identify as "Latinx".