The emperor is portrayed as a wise, just ruler who offers Mulan, implying that he doesn't care about gender. But the plot is kicked off because his army demands every family send a soldier, forcing Mulan to take her disabled father's place. Then she has to hide her gender out of fear of execution. These policies are enforced by what seems to be the emperor's right-hand man, Chi-Fu, but he's the only one who's portrayed as a jackass for them.
Wikipedia tells me the film takes place during the Han dynasty, though I'm not sure how much that narrows it down. I'm mostly just curious if the government in the film's time period had the emperor as the sole or dominant power or if he was simply the head and the actual laws were passed by others.
The Disney adaptation took liberties with the historical setting and details of why Mulan's father was drafted. The original story dates back to the 6th century and was set in the Northern Wei dynasty (386-534). The Northern Wei ruling house were Xianbei people originally hailing from the northeast and ruled over most of northern China- interestingly, the original text of the Mulan ballad uses the nomadic title "khagan" and the Chinese title "tianzi" ("son of heaven") interchangeably to refer to the Wei emperor. Another key difference is that, in the original, the emperor's demand was not for one man from every household, indiscriminately, but called on specific men, including Mulan's father, by name. It also states that Mulan served not for one campaign against a single enemy, but in many campaigns over the course of a distinguished, twelve-year-long army career before returning home and shedding her male disguise.
In this period, China was divided between nomad-ruled northern states and southern states ruled by ethnic-Chinese emigres and warlords. Political division, constant warfare, and social upheaval led to a major split between Northern and Southern cultures, with more warlike and clan-oriented values taking hold in the North and with literary, artistic, and metropolitan values becoming more influential in the South. The story of Mulan fits into the genre of northern "martial songs" which praised military prowess and family loyalty.
In this period in China, both North and South, the decline of state power meant a breakdown in the Han system of a free peasantry which the central government directly levied taxes, labor corvee and military service against, and towards various models of dependency, tenant farming and quasi-serfdom in order to delegate management to lower levels and get by with a less-able (or even absent) central government. One of these forms of dependency was the buqu, a hereditary military household responsible for providing fighting men in lieu of or in addition to their rents/taxes. But the major Northern landlords had become a military aristocracy in their own right, and it seems more likely that Mulan would have come from a warrior-gentry background rather than a servile buqu one (the original poem states that, on hearing the draft notice, Mulan immediately went to market to buy arms and a warhorse, and that she had been trained by her father in martial arts from a young age). But in either case, her father was a man known to the state to have hereditary military responsibilities which could only be passed on to an adult son, a role which Mulan stepped in to fill.