Link to the full text:
https://archives.evergreen.edu/webpages/curricular/2007-2008/psychologyofgender/files/psychologyofgender/Gender%20Constancy-Ruble%20et%20al%202007.pdf
This is what I said on an earlier thread where someone claimed that this paper showed that gender identity is real and nothing to do with sex.
It's clear that the authors aren't actually talking about 'gender identity' as an identity which has nothing to do with one's sex, it's talking about 'sex identity', in other words, the understanding a child has that they are male or female, and that this is a fixed attribute (my bold).
One of the most compelling yet controversial ideas in the gender literature is ‘‘gender constancy.’’ As proposed by Kohlberg (1966), children’s developing understanding of the permanence of categorical sex (‘‘I am a girl and will always be a girl’’) is a critical organizer and motivator for learning gender concepts and behaviors. Slaby and Frey (1975) demonstrated that children move through a series of stages: first learning to identify their own and others’ sex (basic gender identity or labeling), next learning that gender remains stable over time (stability), and finally learning that gender is a fixed characteristic that is not altered by superficial transformations in appearance or activities (consistency). Thus, children are thought to reach a full understanding of constancy once they recognize that they will always be the same sex, across time or change in situation (e.g., a boy who puts on a dress and a long-haired wig is still a boy even though he resembles a girl). These stages have been confirmed in other research, including cross-cultural studies (e.g., De Lisi & Gallagher, 1991).
This is from an article by Katie Alcock (child development specialist) about how the language has changed over time:
What this also means is that terminology has changed. When this area of research first started, everyone knew, and was clear, that they were talking about children’s knowledge of biological sex. The terms “sex identity” and “sex constancy” were used, to mean children’s knowledge of whether they were a boy or a girl, and whether they or others could change into the opposite sex. Around the 1990s everyone started getting squeamish about the word “sex” and started using “gender” as a euphemism. Researchers, however, still meant a child’s knowledge of biological sex.
That paper doesn't seem to contain any evidence for what you are claiming.