What are examples of characters in Shakespeare's Twelfth Night whose actions disrupt the status quo, other than Viola who dresses as a boy?
The term status quo refers to the existing state of affairs; hence, anyone who disrupts the status quo disrupts currently held social and political norms (Collins English Dictionary). One character who also disrupts the status quo, besides Viola dressing as a man, is actually Duke Orsino.
We learn in the very second scene that Orsino is in love with and pursuing Olivia whose father died a year ago and whose brother died only shortly after that. Hence, we learn that Olivia is in mourning, as we learn from the captain who rescued Viola:
[Olivia is] the daughter of a count
That died some twelvemonth since, then leaving her in the protection of his son, her brother,
Who shortly also died; for whose dear love,
They say, she hath abjured the company
And sight of men. (I.ii.37-42)
Customs for periods of mourning differ per era, but during the Middle Ages through Renaissance, mourners could wear their full mourning attire for a long period of time, at least for up to a year, and in some eras even two-and-a-half years. Mourning clothes consisted of all black clothing and even a veil. While in mourning, mourners were not expected to have to mingle with society. Some poorer widows, however, often broke the period of mourning to marry again out of financial need. Since Olivia's brother has died less than a year ago, Olivia has every social right to be in mourning right now and to reject the company of all society, especially men who are trying to marry her for financial gain.
Hence, one way in which Duke Orsino is disrupting the status quo is by attempting to court Olivia while she is still in her period of mourning. Since he is being so heartless as to disrupt her mourning period, it's no wonder that she has rejected his marriage proposal.