It is such an appropriate point to bring forth.
Children begin to identify the basic gender differences at just a tender age of three. From the time they're born, they're compelled to abide by some gender-specific performance which makes them believe what they're doing even if they would be unwilling to do so later in life.

Children are often scolded if they choose to do things that don't conform to the social rule of gender identity; this evokes confusion about their true identity, which can affect them in future.

So it is definitely necessary for parents to choose gender-neutral parenting.
There are some negative aspects of gender stereotypes for children.
Like when children begin to limit their choices according to the set gender rules, they often cultivate the qualities and skills only acceptable to their gender.
This would eventually make them lose their complete development. Like girls taught to become submissive would become quieter, and boys would inherit the qualities of competitiveness and aggressiveness to prove their manhood.

And the other children who lie on the opposite side of the discussion who would choose not to conform to gender conformity will be bullied and ostracised from society.

Hence, it's a role of society as a whole which definitely begins with parents to create awareness about gender-neutral parenting so that everyone can support gender non-conformities with happiness.