This is the most lightweight example possible. Here's some more:
- makeup being for women and not for men
- dresses and skirts being for women
- high heels literally used to be for men
- any profession being "for women" or "for men"
There are some grey areas that are probably an intertwining of biological and social gender:
- women being the predominant childrearers for very young children (both in the family and in creches)
Some things are a combination of historical social constructs, social gender constructs, and biological gender
- men being the predominant wage earner while women are home makers
(the part of this that is related to biological gender is that women need to take more time at home to take care of very young children, everything else is a social construct).
Some very few things remain as pure biology:
- pregnancy and childbirth
... although even these are surrounded by all kinds of social constructs, such as most midwifes being women.
If you can say one thing about the nature/nurture debate it's that human beings - as a species, not necessarily as individuals - are incredibly flexible and adaptable, and only the most basic of things are absolutely fixed by our biology and genetics.
I say that "race is a social construct" but not "gender is a social construct", because gender has both social and biological components.
Gender having a biological component does mean that gender stereotypes that the average person learns are based on biology. The concept that pink is for girls and blue is for boys is social and cultural, not biological. Gender having a biological component is more complicated. A good book that explains this is Whipping Girl by biologist and trans woman Julia Serano:
https://en.m.wikipedia.org/wiki/Whipping_Girl
The first tenet of this model, the model's core that everything that follows is built upon, is the fact that "subconscious sex, gender expression, and sexual orientation represent separate gender inclinations that are determined largely independent of one another."
Just like cisgender women, not all trans women are "girly".
The fourth and final tenet of this model states that "each of these inclinations roughly correlates with physical sex, resulting in a bimodal distribution pattern (i.e., two overlapping bell curves) similar to that seen for other gender differences, such as height." This idea is what allows for the natural exceptions to gender expression to exist within the system without attempting to claim that they exist in as high of numbers as typical gender expression.