One of my favourite things to do while watching a show (or commercial) is to switch the gender of the person, I've done it a lot on Bones, everything about them stays the same they just get the opposite gender. Most of the time I come to the conclusion that the character would work in the opposite gender and sometimes I even think it would be more interesting that way.
For example the other day I saw a commercial about a man driving a car and he was singing/rapping along and I imagined him as a female instead. Normally we don't let women be so natural and most of the time we don't even let a woman drive the car in a commercial so I thought to myself that I would have found the commercial so much more cool if it had been a woman - gone against the gender stereotype you know, instead of the classic white dude.
Right after was a commercial for chocolate which of course had a woman being sensual with a piece of chocolate and I re-imagined it as a male sitting there with closed eyes holding the piece of chocolate between his fingers. Most people would immediately feel that is weird, that it must be a parody because we cannot see a man in that position (unless of course it's a parody or to show the gender disparity in media). Why? Because basically it's stereotypically more feminine and it's based on the male gaze.
It's not unheard of though to switch a male character to a female one. I think the most famous one is Ripley in Alien which at first was written for a male character but then switched to a female one without them changing anything about the character. It is however more common to go male to female, I don't even know a single character that have gone from female to male - if we don't count the numerous roles that goes to men overall.
That is why when I write I try to pick the other gender than what I, by instinct, chose for a minor character. For example, I needed a head guard and when I wrote it I thought a male character since it's so ingrained by society to be a male occupation but quickly changed to female to challenge the stereotype for both me and reader. Another example: I mentioned a gossipy store owner at one point and in my head it was a female since that is what we naturally think of when we think of a gossipy person so I changed it to a male store owner.
I think we need to challenge this more. Traits and behaviour aren't female or male, they don't come with a gender stamp on them so a character can be either or, but we just need to allow ourselves to see beyond the tiny box we give genders.
We especially need to broaden the possibilities for female characters to be more goofy, funny, caricatures and you know like the characters men have played forever in sitcoms. It has started to broaden, for example Amy Schumer comes to mind, but we need more on the mainstream media.
With that said, male characters also need to be broadened, especially into sensitive areas and traits that are usually seen as female without it being ridiculed or looked down upon. Why not an FBI agent who likes to knit or stay at home dads or men who help out at home without being called pussy whipped every time.
Also, it would be nice to throw out the trope of the lazy, mediocre looking, rather dumb dad who cannot do shit at home while he's married to a smart, gorgeous woman who does basically everything while he's doing crazy shit which she always forgive him for, my best example: the TV-series According to Jim.
If you know any good shows or movies that challenge genders and stereotypes send them my way, I'd love to see them!