Since I haven't actually done much in the way of gender studies, this is all going to be personal/anecdotal in nature. Please observe tiny Sarah playing with a dinosaur (never a Barbie)...
...and then, 10-year-old Sarah, who closely resembled Simon from 7th Heaven. (And yes, this preacher's kid totally watched that show.)
There was about a decade of my life where I refused to wear dresses. I kept my hair as short as my parents allowed, wore boys' clothes, played sports and spent a lot of time in the woods. I didn't know that I wasn't performing my gender "correctly"; I just knew I was having more fun than the girls who were worried about getting their dresses dirty.
Although my parents (thankfully) drew the line when I begged to get a buzz cut, I don't have memories of them trying to correct my gender performance at all. Dad played basketball and softball with me, and Mom allowed me to stick with sports bras at first when that awkward life phase came around. They bought me dress pants instead of skirts to wear to church and let me go to all-boys' birthday parties. Come to think of it, I've never asked if my tomboyishness ever concerned them, but it was just a part of who I was until about middle school (AKA the worst three years of just about everyone's life). Thanks, Mom and Dad, for loving tomboy Sarah!
Now, I realize that the folks who made this commercial probably weren't trying to make some major statement about gender, and one friend pointed out that they were probably making fun of the mom. Besides, I realize that at least some of that kind of anxiety on the part of parents has to do with concern for their kid's well being. Was I teased for dressing and acting like a boy (whatever that means)? Absolutely. I've never thought about it much, but I still have residual insecurities from high school and even before that might have been lessened had I socialized myself more femininely from an earlier age—but then again, maybe not. Maybe it simply would have introduced those insecurities sooner.
I've never been a parent, and anyway this isn't a parenting advice column. But I find traditional gender roles problematic in many ways, and we as a society and as a church need to recognize how deeply entrenched these assumptions are and how they can be destructive. If the church only had women like the mom in that commercial, I would scream. (I want women like that mom in the church. I just also want women like the little girl in the church.) I've seen churches and youth groups especially that sometimes reinforce these expectations in such a way as to become exclusive; some of my more difficult memories from high school have to do with feeling like I wasn't pretty enough by the standards of the girls with whom I went to school and church. Having been a youth pastor briefly, I've talked with other youth leaders about how even compliments on one teenager's hair or clothes can create an unsafe space for others if we aren't careful.
If your daughter prefers Legos over Barbies, buy her Legos! We need more women in math/science/engineering anyway. (Not me.) And if your son insists on wearing a tutu everywhere he goes, let him. Heck, Jesus wore a dress.
For the record, although I perform my gender more "correctly" now, I am currently wearing a pair of men's sweatpants that I bought myself, and they are SO comfortable.