Director Pete Docter and Pixar founder John Lasseter explain why Riley's emotions are mixed while her parents' are not.

First, the parents' emotions are due to both emotional development and story and acting flow:

I [Docter] remember, we talked to John and he said, ‘Well, I thought you did it because, as adults, we become more kind of set in our ways. As a kid, you can... anywhere is possible.’

 

Docter said that they were ultimately two things that were absolutely vital to the scene: clarity and comedy. Had Riley’s parents both had multi-gendered emotions like their daughter, the scene would have been going back between 18 different characters, and it was a bit unruly unless everyone was identifiable. Not only did making the emotions gender specific in the parents make the sequence easier to follow, but it also opened up an opportunity to create a few extra laughs.
Explained the director:
For the comedy of it, we’re cutting between 18 characters and 4 locations in that dinner scene, so we just went broad with it - kind of how SNL would do it. They all have like dopey obvious mustaches or big red glasses so that you’re instantly clear on, ‘Oh, it’s mom; it’s dad.’ http://www.cinemablend.com/new/Why-Inside-Out-Main-Character-Has-Male-Female-Emotions-72176.html

So the parents are simplified to make the scene easier to follow, and because as Adults, they have already developed their adult personality/emotions. Riley has not yet.

Interviewer: What was the thought process behind the genders of the emotions?
Docter: Again, it was intuitive. It felt to me like Anger's very masculine, I don't know why. And then some of it came to casting... Sadness felt a little more feminine and Mindy Kahling as Disgust felt right. And someone balanced too. Plus the female roles lead because it's inside a girl. With mom and dad, we skewed them all male and all female for a quick read, because you have to understand where we are, which is a little phony but hopefully people don't mind! http://www.empireonline.com/empireblogs/empire-states/post/p1463

So in short, Riley's emotions are mixed because, as a pre-teen, she's likely not to have developed a strict outer personality. She's still growing, and developing her own style. She's still raw and malleable, impressionable. Secondary to this is of course the rule of funny. Having some of the emotions as male is purely for show.

Director Pete Docter and Pixar founder John Lasseter explain why Riley's emotions are mixed while her parents' are not.

First, the parents' emotions are due to both emotional development and story and acting flow:

I [Docter] remember, we talked to John and he said, ‘Well, I thought you did it because, as adults, we become more kind of set in our ways. As a kid, you can... anywhere is possible.’

Docter said that they were ultimately two things that were absolutely vital to the scene: clarity and comedy. Had Riley’s parents both had multi-gendered emotions like their daughter, the scene would have been going back between 18 different characters, and it was a bit unruly unless everyone was identifiable. Not only did making the emotions gender specific in the parents make the sequence easier to follow, but it also opened up an opportunity to create a few extra laughs.
Explained the director:
For the comedy of it, we’re cutting between 18 characters and 4 locations in that dinner scene, so we just went broad with it - kind of how SNL would do it. They all have like dopey obvious mustaches or big red glasses so that you’re instantly clear on, ‘Oh, it’s mom; it’s dad.’ http://www.cinemablend.com/new/Why-Inside-Out-Main-Character-Has-Male-Female-Emotions-72176.html

So the parents are simplified to make the scene easier to follow, and because as Adults, they have already developed their adult personality/emotions. Riley has not yet.

Interviewer: What was the thought process behind the genders of the emotions?
Docter: Again, it was intuitive. It felt to me like Anger's very masculine, I don't know why. And then some of it came to casting... Sadness felt a little more feminine and Mindy Kahling as Disgust felt right. And someone balanced too. Plus the female roles lead because it's inside a girl. With mom and dad, we skewed them all male and all female for a quick read, because you have to understand where we are, which is a little phony but hopefully people don't mind! http://www.empireonline.com/empireblogs/empire-states/post/p1463

So in short, Riley's emotions are mixed because, as a pre-teen, she's likely not to have developed a strict outer personality. She's still growing, and developing her own style. She's still raw and malleable, impressionable. Secondary to this is of course the rule of funny. Having some of the emotions as male is purely for show.