TERFs are generally opposed to the idea of stating pronouns and doing pronoun rounds.
Personally I have no problem with people not stating their pronouns. I sometimes forget, and I notice trans people sometimes also forget.
So why have pronouns become such a flashpoint for the TERF community?
For many of them, the stakes are very high. For example, Holly Lawford-Smith, author of the embarrassing book “Gender-Critical Feminism” states that, “Reclaiming the word ‘woman’ for female people, and reserving the use of sex-based pronouns for people who actually have the sex, are helpful tools in getting feminist theory and movement back on track as being fundamentally about sex caste.” - Holly’s blog
What TERFs seem to want to say is that pronouns ought to be associated with a sex. However, we know language is not objectively biological: he, him, she and her are not universal terms used by every human. This seems to place pronouns firmly in the “gender” category, and it’d seem that both TERFs and the rest of us would agree, that gender is a “social construction”.
So if we both agree that pronouns are not biological, it’d seem that there’s no objective reason to apply a particular set of pronouns to someone. In fact, ascribing a non-standard set of pronouns to someone would seem to be “gender non-conforming”.
However, if pronouns are biological, not doing pronoun rounds seems to imply something pretty regressive and unscientific: the idea that a person can immediately tell what sex someone is from the way they look. This undermines the ability of butch lesbians, femboys, and all kinds of gender non-conforming people to comfortably exist in the world, regardless of how a person feels about trans people.
TERFs talk a lot about how much they support gender non-conforming people. But, how exactly are these people non-conforming if they don’t undermine societal expectations of what they are called and how they appear? What exactly are they rebelling against?
As a final point, accepting pronouns and pronoun rounds demonstrates that trans people don’t think you need to look a certain way to be called a certain thing. Trans people are the true gender non-conformists and are allied with gender non-conforming people.
Stating pronouns and doing pronoun rounds undergird the belief in, and support of, gender non-conforming people. Stating your pronouns makes no claim about the veracity of gender stereotypes, and in fact, undermines them.