Many pacific island countries on now socially quite conservative (for example, they would think a woman running in running shorts to be inaproriately dressed). Was this the case before Christian (and Morman) missionaries arrived?
I can't answer with regards to polynesia as a whole, or about gender norms with regards to clothing, but in Hawai'i the "kapu" system of taboos dictated behavioral norms for interactions between social class and gender.
Generally, the kapu system was based on a cosmology that saw male elements as sacred and female elements as profane. So there were a variety kapu related to keeping male and female people / things seperate. It was kapu (taboo) for women to eat in the presence of men and it was also kapu for them to eat masculine foods such as pork, coconuts, and bananas. Likewise it was kapu for men to eat feminine food.
The kapu system was eventually abolished starting in 1819 when Liholiho (Kamehameha II) shared a meal with his mother and stepmother, symbolically ending the taboo.
I don't think this fully answers your question but the kapu system in Hawai'i suggests that socially conservative gender norms predate Christianity (at least in Hawaii).
Source:
Levin, S. S. (1968). THE OVERTHROW OF THE KAPU SYSTEM IN HAWAII. The Journal of the Polynesian Society, 77(4), 402–430. http://www.jstor.org/stable/20704579