In what ways might gender affect the distribution of of social customs in a community?
This depends to a large degree upon the community. Gender roles display great degrees of variation across different cultures and periods.
One of the first ways in which gender role variability affects social customs is the degree to which genders have distinct activities and behaviors. For example, ancient Greece was known as what we would call "homosocial." In other words, adults mainly socialized with people of their own gender. This was closely related to the differentiation of economic roles, women being responsible for weaving and cooking, while men were responsible for economic, political, and military activities. This led to customs such as "symposia," parties in which men (and occasionally prostitutes) gathered for drinking, dining, entertainment, and conversation. This strong separation of genders may have led to pederasty, a custom in which older male lovers acted as mentors to their younger male lovers.
Distinct gender roles and the importance placed on hereditary privilege often leads to arranged marriages and customs forbidding unchaperoned meetings between men and women. Many of the social customs we see in Jane Austen, such as balls and afternoons "at home" where people met to drink tea, were arrangements that allowed for the preservation of female virginity while arranging marriages.