Kids are hardwired to figure out who they are and how they fit in, and by an early age they have figured out gender and what that means - it's one of the first layers of identity. Studies have shown that even when the parents have very liberal gender views, kids still see past that to the wider societal view.
I am not convinced, personally, that this is a huge problem. Children conceptualize very broadly when they are young, and as they mature, they begin to see individual differences. As long as parents are very open to individual differences as their child develops, that early understanding should not be prescriptive of how they must behave, while it will alert them to areas of difficulty they will encounter if they don't conform to norms. This may help them protect themselves from ridicule as they explore identity.
A recent study about gender and toy preference determined that even when parents thought they were not influencing their children's toy choices, the children identified toys by "gender" as ones their parents would approve of or not. Here's an excerpt from the study:
Young Children’s Construction of Gender
Children construct their understandings of gender at an early age. By
about 24 months they begin to define themselves as ‘‘girls’’ or
‘‘boys’’ (Kohlberg, 1966; Kohlberg & Ullian, 1974; Sandnabba &
Ahlberg, 1999). And they are apt to have rigid definitions of how
girls and boys should behave by the age of five (Martin & Ruble,
2004). The acquisition of these gender stereotypes demonstrates that
children are very effective students of culture. They quickly learn to
categorize ‘‘girl toys’’ and ‘‘boy toys’’ in socially acceptable ways
and to behave as they think they ‘‘should’’ (Raag & Rackliff, 1998;
Powlishta, Serbin, & Moller, 1993). Preschoolers have been shown, for
example, to reliably apply gender stereotypes when responding to
questions about how their parents, teachers or babysitters, peers, and
siblings would want them to play. Girls know they are expected to play
with dish sets and baby dolls and boys know tools, trucks, and cars
are for them (Raag & Rackliff, 1998).
The authors of some studies have noted that society’s definition of
what is feminine has expanded since the launch of the women’s movement
in the early 1970s, but the definition of masculinity has not been
similarly revised (Fagot & Littman, 1975). This line of inquiry has
documented that while the current generation of girls is more likely
to be encouraged to do things that were once considered masculine than
were their mothers, the past 20 years has seen both children and
adults narrow their definitions of appropriate behavior for boys
(Burge, 1981; Cahill & Adams, 1997; Fisher-Thompson, 1990; Martin,
1990; Moulton & Adams-Price, 1997; Turner & Gervai, 1995).
How are Children’s Cross-Gender Behaviors Perceived?
Researchers who describe adults’ and children’s typical responses to
cross-gender play consistently report that boys who engage in ‘‘girls’
games’’ are more likely to be criticized by parents, teachers and
peers than are girls who enjoy activities and materials labeled as
‘‘for boys’’ (Cahill & Adams, 1997; Martin, 1990; Martin, 1995;
Martin, Wood, & Little, 1990). These results have been interpreted as
evidence that adults share concerns that boys who exhibit cross-gender
behaviors will become increasingly feminine, but believe that girls
will outgrow their ‘‘tomboyishness’’ and will become as feminine as
their ‘‘typical’’ female peers (Sandnabba & Ahlberg, 1999). It has
been documented, moreover, that fathers often more rigidly impose sex
role expectations on their sons than on their daughters, and that they
are less flexible in their definitions of gender appropriate behaviors
than are boys’ mothers (Burge, 1981).
Freeman, Nancy. "Preschoolers’ Perceptions Of Gender Appropriate Toys And Their Parents’ Beliefs About Genderized Behaviors: Miscommunication, Mixed Messages, Or Hidden Truths?" Early Childhood Education Journal 34.5 (2007): 357-366. Academic Search Complete. Web. 22 Dec. 2013.