Martha as Mammy and yet more 'ism's in the Whoverse.
And really, were we talking about sexism and its stereotypes as framed for white women they might have a leg to stand on but sexism isn't a one size fits all sort of a category. Portrayals of women (and the attendant sexism) vary greatly depending on the race of the woman. Generally speaking young white women have options in terms of being chaste/being sexy and being heroines or being painted as damsels in distress. That's because the key word there actually isn't the distress part. It's the word damsel. Damsels are always desirable, no matter how much ass they kick (or don't) and nothing they do makes them unworthy of love or protection.
The stereotype start to swing in whole new directions when it comes to other ethnic groups. Latina women (assuming you can find many on TV) are usually either oversexed or completely sexless with a large number of children. If they have Latino boyfriends/husbands the men are usually portrayed as criminals or at best overtly chauvinistic. Mostly though they aren't portrayed at all. There have been some exceptions, but not many and mostly those exceptions are in sitcoms. Asian women get to be sexy or smart, but generally not both and they certainly don't have relationships with Asian men. But hey, Asian men aren't usually portrayed at all or if they are the options are sexless, king fu master, or geek who is obsessed with sex. Doubt me? Find me ten Asian male characters that don't fit any of those molds. Same with Latino men. And just look at Tosh on Torchwood for the Asian woman stereotype that keeps screaming at the top of its lungs. You can also look at Lucy Liu in Ally McBeal.
Now, let's talk about black people. Black women tend to get two choices. Mammy or Jezebel. Occasionally the third option of Sapphire (see nagging shrew constantly emasculating a weak black man) rears its ugly head. But mostly the choices are asexual Mammy or nympho Jezebel. And yes, Martha is smart and she comes from a good family and really it's not like we see her or her family running around as servants complete with little uniforms...oh wait. Let's start with the portrayal of Martha as Mammy (see her taking care of the Doctor repeatedly including being a maid for three months but also working to support him in the 1960's), no agency of her own to speak of when it comes to saving the world (particularly when you note that the grand plan amounts to her telling everyone to clap to save Tinkerbell) and then let's talk about her spending the entire season being made to feel like second best. She even gets the dubious joy of being told directly not to get above herself in Human Nature/Family of Blood. And I suppose the argument could be made that the characterizations were appropriate to the time of 1913.
However that doesn't tidy up the rest of the season where Martha alternates between flirting* with every available white man that crosses her path, pining after the unattainable Doctor and sacrificing her pride to save the Great White Hope. Martha's repeatedly laying it all on the line for a guy that treats her like crap, and I don't mean his lack of interest in a relationship. I mean his telling her (even after it's clear that Saxon is the Master) that she doesn't need to know anything else about him, or the screaming at her (which happens a few times, but most notably in Utopia) and even the point at which she goes out to get them all dinner while he and Jack hide out in the Warehouse in Sound of Drums. Martha isn't being protected, she isn't treated as a damsel. It's the Strong Black Woman/Mammy myth complete with the idea that she is supposed to be willing to sacrifice everything to protect the ones that can actually do some good. Theoretically I suppose the flirting is supposed to ameliorate the Mammy stereotype, but each time the flirtation is almost completely unconvincing (What is it with the guy in 42 flirting back, but then looking utterly shocked when she snogs him?) and there is no hope of the flirtation going anywhere. On an individual level the incidents aren't that bad, and could conceivably be construed as germane to the story.
But that doesn't explain the treatment of Tish and Francine. The portrayal of Francine as the Sapphire stereotype complete with the emasculated husband (who incidentally gets to be portrayed as a janitor) and Tish as a Jezebel that manages to get the hots for a man that was in his 80's a scant ten minutes earlier who has a wife no less is particularly telling. In fact we are told repeatedly that Tish is getting jobs for which she isn't remotely qualified solely as part of Saxon's master plan. He even tells her at one point that her job is to stand around looking pretty, which really made me wonder about sexual harassment laws in the UK. Yet he has no interest in capitalizing on Martha's relationship with her brother or her father until her Dad makes the effort to warn her. And you know, Tish didn't particularly strike me as a stupid girl when she and Martha were helping to stop Lazarus, so why wouldn't she be qualified for the PR job? She certainly seemed to manage to put together a beautiful gala in very short order. Martha's dad manages vaguely to attempt to fight back, but it's clear he isn't actually seen as being anywhere near as much of a threat as Jack. And Leo seemingly disappears completely from every one's mind. No strength or heroism to be found in him at all. And it's not just Martha's family that gets short shrift.
Let's not forget Mickey being portrayed first as ridiculously cowardly (cowering behind Rose's legs and then being called the idiot for most of his appearances) ala a whole host of racist stereotypes including the old favorite of Step and Fetchit. In fact even when Mickey manages to grow a pair and break it off with Rose it's still made very clear that he's useless, and he only manages to gain redemption by abandoning his entire life (which again apparently wasn't worth much anyway) and sidestepping into an alternate universe. One in which apparently he's still content being Rose's tin dog. There are very few character's of color in the Who verse to begin with, and for all of them to fit so neatly into various stereotypes? At some point that's not accidental nor is it germane to the story. Is it meant to be overt racism? No. But it fits the definition of aversive racism very nicely, as does the insistence of much of white fandom that the POC are seeing things that aren't there. Sometimes the people who regularly have to experience racism? Know it when they see it. And when the white fans that also see it say "Oh my yes, it's clearly there?" Then the Emperor is not wearing new clothes and carrying a bouquet, he's naked and carrying a noose.
*I found it quite interesting that she never managed to be attracted to a single man of color, and neither was Tish. The Whoverse is mighty white even in the depths of space. In Gridlock the young couple trying to make a life involves a WOC and a white man. Newsflash, sometime POC date other POC. No really, and we make lovely successful families too. Also shockingly some MOC don't pine after white women.