Things like that did happen. There's a picture of Marlene Dietrich arriving at a railway station in France before WW2 and she's in a trouser suit, looking very fashionable and daring with a crowd of hangers on (all male), but moments later she got arrested. I have seen photos of a female climbing club in La Belle Epoque, ascending a tough rock face in long dresses (I am told they sometimes climbed in knickers when blokes weren't around because the dress was heavy and cumbersome. So whether you got away with pushing the frontiers of public sensibility was always the same as now. Fame, wealth, confidence, support, opportunity.
Same with ancient Rome. Women were expected to be demure and dutiful, but as Rome got wealthy on the back of conquest, so women started taking risks and pushing at social boundaries. One lady called Sempronia absolutely shocked polite society but a generation later in the Principate, her antics would only have raised an eyebrow.
We have women like Julia, Augustus' daughter, who was so annoyed and frustrated at her father's moral crusade and stifling family atmosphere that she rebelled and became very wayward. Eventually her father found out about her hedonistic lifestyle and was so angry he had her exiled to a small island. The public heckled him in the street to bring her home.
Or Agrippina the Younger? Never overt, but a woman who had gossip and controversy follow her like attendants. Did she sleep with her brother Caligula? Was she trying to get off with her son Nero at a social dinner? We don't know.
Or on a different theme, Julia Ferox in Pompeii, who after the death of her husband hired out her home as a social club and apparently did roaring business.
But - and I say this advisedly - it is interesting that clothes were labels as much as accoutrements to the Romans, and taking a privilege you weren't entitled to, or trying something new was worse than actual bad behaviour.