One argument can successfully be made that gender roles in Twelfth Night, inclusive of Viola's switch to Cesario, show that the particulars of romantic love are common to both genders. For instance, Orsino and Viola and Olivia all fall in love at first sight. Another argument can be made that, similarly, the particulars of character traits are common to both genders even though they are identified by different terms. For instance, Viola as Viola is loyal and devoted, whereas, Viola as Cesario, while exercising the same character traits, is persistent and determined.
The major commentary on gender roles has to do with the two role reversals, which are that of Viola into Cesario and that of Malvolio into the oddity that Maria prescribes as being desirable in the counterfeit letter presumably written by Olivia. For instance, while Viola is the male Cesario, she/he is importuned (hounded) by Olivia to further a suit for her hand in marriage. Typically, the stereotyped gender role prescribes a submissively waiting female, who, in this gender-reversed case, is Olivia.
In another instance, Malvolio abandons his tastes, habits, preferences, and even wardrobe then dresses to please the object of his affection (or so he thinks). The typical stereotyped gender role in this scenario is for the female to abandon her tastes, habits, preferences and even wardrobe to suit the actual or supposed desires of the male object of her affection. [Incidentally, this stereotyped gender role was complained about by Tolstoy and is still alive and thriving today and reveals itself in stilettos, pencil skirts, etc.]