One specific example of the backfiring of identity politics usage by the left that I know of that is backed by several research studies is the introduction of the term "latinx" in the mid-2000s in an effort to bring gender neutral language to the term that represents US Latinos because Latino/Latina only represented guy/girl. The Pew Research Center found that most Hispanics oppose the term.
https://www.pewresearch.org/race-and...x-and-its-use/