Which is not to say you're wrong, or that specific stereotypes don't, no doubt, exist in some people's minds, just to say that the "trying to make a good impression on the nightmare in-laws" is a comedy of manners stock-plot that plays about like that with every other ethnic combination.
If we're going to talk about potentially harmful stereotypes used for humor, the gender dynamic between Spock's in-laws is fascinating. T'Pring's
mother is a bigoted harridan who uses her husband's family honor to rationalize and reinforce her own prejudices-- simultaneously very Vulcan and
very human-- while her father is a good-natured, open-minded, and
spineless doormat who capitulates his supposed domestic authority in order to protect the mere illusion of it.
It's a sitcom premise with sci-fi execution, and it's brilliant. Also, if you imagine that T'Pring's father had gotten Pike alone for five minutes-- he would have asked Pike to give
Spock those recipes, so that his household staff could truthfully say
they got them from a Vulcan.
I'm not a fan of nuTrek style grimdarkness, but I like episodes like this (or Una's court martial) that show that the cultures and the species of the Federation still have foibles and feets of clay... because Roddenberry's utopia shines the brightest when the franchise reminds us that
utopia isn't easy, that
everything that
Star Trek tell us is
possible had to be fought for tooth and nail by us and our children, and zealously guarded by their grandchildren's grandchildren.
Everything our heroes in Starfleet have to fight for in their utopian future is a reminder that
their ancestors brought them
there from a world that was even darker than
here.