Q:

How did women's roles and rights change during the early Republican period in China?

How did attitudes towards women and their role within the family unit and greater society change under the Chinese Republican government? What rights did they gain? Did they generally benefit from the Republican era? 

A:

Keep in mind that most of China was controlled by local warlords (or Imperial Japan) throughout much of this period. A lot of the time there wasn't much of a "under the Republican government" to speak of since they were effectively ruled by regional strongmen. However, generally speaking, women (particularly those from literati families) experienced a political awakening. Significant, albeit slow, improvements in women's daily lives took place over the decades.
That is, if we ignore the extremely adverse effects of the incessant warfare of the period.

The late Imperial and early Republican period was a time when Chinese elites turned away from traditions in favour of western ideas. This westernisation process was attempted for all spectrum of society from daily life, to the economic structure, and the political system. Lifestyle (for the gentry, at least) westernised the fastest and earliest.
Most people are probably aware of the abhorrent practice of foot binding. This is one of the most significant women's issues during the early Republican period. By the late Imperial period, liberals had begun to regard foot binding as the senseless crippling of half the population. Soon after the revolution, initiatives were implemented to combat it: President Sun Yat-sen issued an edict in 1912. A more comprehensive order that provided for inspectors to ensure compliance was promulgated in 1927. Though progress was slow, foot binding was gradually stamped in most of China near the late 1940s.

(Illustration of bone deformation during foot binding, from Tensoku Monogatari by Okamoto Ryuzo)
The Republican period also saw a relaxation of public decency standards, including attitudes towards sex and sexuality. As late as 1920, exposing forearms or calves were still illegal, not to mention any décolletage. Attitudes changed drastically over the rest of the decade, however. Scholars returning from studying abroad brought with them a spark of sexual liberation, such as Chang Ching-sheng whose 1926 Sexual History sparked a massive storm. Importation of western fashion styles, particularly in the major port cities, led to comparatively much more revealing dresses for women.

(Left: Promotional poster for cigarettes, Shanghai, circa 1930s | Right: Earlier poster for milk; notice the flattened chest. )
These changes in attitude led to a suppression of the custom of breast binding. Though much less abusive than foot binding, flattening the breasts of women had been prevalent as an expression of traditional Chinese aesthetical preferences. As attitudes changed, demands to end the practice began to appear, culminating in a 1927 rally in Wuhan that shocked public sentiments with displays of nudity. The Nationalist government in Canton banned breast binding in the same year, and tasked police officers with enforcing fines on relatives of women with bound breasts.

Such lifestyle changes were accompanied by a general rejection of traditional Confucian morality. In the case of women, Confucianism dictated obedience to male figures as well as general ignorance. The latter in particular were challenged towards the end of the Imperial period, when liberal elites argued that the ignorance of women was a key factor in China's backwardness. More generally, the extreme gender inequality of traditional society was contrasted unfavourably with European Great Powers. Even before the Republican revolution, therefore, women such as the tragic heroine Ch'iu Chin had begun advocating equality for women.
These trends picked up momentum during the early Republican era. The May Fourth Movement, which broke out in 1919 in protestation of Japanese demands at Versailles, is sometimes regarded to have heralded the start of popular feminism in China. Many of its leading intellectuals wrote of the need for the "liberation" of women. Chen Tu-hsiu urged women to take back their independence, and partake in politics as distinct individuals (as opposed to obeying their husband or father's politics). Li Ta-chao, another promoter of the New Cultural Movement, argued that true democracy requires the liberation of women. He promoted the adoption of Western-style small, monogamous families where, he believed, women would be better respected than traditional large, polygamous Chinese clans.

(Women attending school after the May Fourth Movement, adopting the dress styles of their male counterparts)
Before 1919, only nine secondary schools for women operated in the entirety of China. Only three private (church-operated) universities allowed women to apply for study. After 1919, and somewhat buoyed by the surge of activism (among both men and women) during the May Fourth Movement, universities across China began lifting their bans on female students. The Peking University began admitting women as formal students 1921 (the previous year it allowed women to "listen in").

Traditional Chinese marriage was heavily controlled by parental designs. In the early Republican period, romantic love and free marriages started to become fashionable as virtuous choices. Age-old traditions, such as concubinage, became frowned upon as uncivilised practices. The Republican Civil Code issued in 1930 formally forbade taking concubines (or polygamy in general).
Actual changes should not be overstated, however. Planned marriages remained the norm in most of t China. Although anything other than monogamy was formally disallowed, in practice the central government could only unevenly enforce this upon its own officials. Concubines remained a common occurrence in general until after the Republican period ended.
The role of women were also barely changed. By the 1930s, the government endorsed New Life Movement had sprung up as a reactionary response to leftist ideologies. The policy squarely pegged women as serving domestic roles within the family unit, as a "force for improving the family". For instance, Generalissimo Chiang Kai-shek's wife, Soong May-ling, called upon educated women to teach their neighbours how to manage affairs at home and raise the children.

Politically, the cause of feminism faced stringent opposition from more conservative elements of society. Despite taking part in the revolution against the Manchurian court, and being recognised for their role, women found themselves excluded in Republican politics. Mere months after the revolution, a gender equality clause became conspicuous by its absence in the temporary Republican constitution of 1912. This is despite promises of equality the revolutionaries had made to the women in their ranks, notably by temporary president Sun Yat-sen on 5 January. His promise was lambasted at the time and died with his abdication to warlord Yuan Shikai.
A gathering of Nationalist representatives in 1924 declared one of their goals to be the "establishment of the principle of equality for women in law, economy, education, society, and to promote the development of women's rights". This promise was only partially fulfilled in 1947, when the Republic adopted a constitution declaring all citizens, regardless of gender, to be equal under the law. That said, due to the lack of a functional democracy throughout most of the period (and beyond), the delays on this issue had limited practical significance.

