Seth Menachem wrote a wonderful parenting article called, "So my son wears a dress; What's it to you?" He isn't a stoic, to my knowledge, but he certainly presents a strong example for anyone attempting to stand up for rationality in the face of irrational social norms.
Away with the world's opinion of you—it's always unsettled and divided.
Seth's two year old son happens to prefer dresses at the moment. Like so many two year olds, the child can express that preference in a way that wears on his parents nerves. During one episode, set off by Seth's attempt to steer his son towards "boy clothes" he had a wise realization.
"[Asher] had a huge tantrum as I tried to force his legs into a pair of shorts. His nose was running into his mouth as he cried and protested and I suddenly realized I was fighting for something I didn't even believe in. I was making my kid feel badly for something he shouldn't be ashamed of. And I stopped."
Dad had been worried about what other people would think. Suddenly, he realized that what those people think is their problem. Dad's problem, his duty, was to be a father to his son, raise him well, and enjoy life in the process. So Seth did the rational thing, he let his son wear the dress. Little Asher continues to wear dresses in public, and continues to raise eyebrows. Seth doesn't shoulder the burden of those judgments. He runs into obstacles, but he faces them all very well, one might say he faces them stoically.
I have a daughter, so it's unlikely that I'll face the same sort of social friction. Freyja could wear jeans and a t-shirt every day of the week and no one would bat an eye. Not that I don't run into my community's gendering issues all the time. Take any ten month old with short hair out into the world in any color other than pink or purple and you won't have to wait long for the masculine pronouns to roll in. But that's just knee-jerk reactions, no one continues on to question my parenting simply because my daughter is wearing forest green.
Read the article. You'll find great examples of stoic judgments and actions in a modern context. Seth's older daughter even acts like a philosopher of old and gets her dad to face some real potential embarrassment! Good stuff.