Every person you ask is going to have a different response to this question.
What it boils down to in my opinion is this: there is no law that says a nonbinary person must completely reject any and all associations with the binary genders.
Being nonbinary just means that our genders are other or more than one of the two binary genders. Being nonbinary does not mean that we have to reject all binary gendered language, names, and actions.
Nonbinary people can:
-use she or he pronouns
-be girlfriends or boyfriends
-be Mr. or Ms.
-be sister or brother
-wear traditionally gendered clothing
-take testosterone or estrogen
-refer to ourselves as boys or girls, men or women
-be transmasculine or transfeminine
-still feel some connection to our assigned gender
-align with a binary gender for personal and/or political reasonsAnd still be nonbinary.
These things do not belong to the gender binary. Not all nonbinary people want to be androgynous in appearance, have gender neutral names, and go by they/them. Not every nonbinary person considers themself to be a distinct third gender. Some nonbinary people have fluid or changing genders that include the binary genders. Some nonbinary people embrace concepts of nonbinary manhood or nonbinary womanhood.
Every nonbinary person is different.
There is this myth that “nonbinary” is a single androgynous gender. And that isn’t reality. Nonbinary is an umbrella term for a group of people who often have complex gender identities, relationships with gender, and (but not always) gender dysphoria.
Tl:dr
Nonbinary identities are not necessarily exclusionary of the binary genders.