A couple of days ago, I was having a conversation with a professor of Shinto Studies at Kokugakuin University, and the subject of female priests came up. His speciality is the period 1868 to 1945 (a clearly distinct period of Japanese history), and what he had to say was interesting.
Apparently, in the late nineteenth century, there were female priests at some jinja. This happened because, with the separation of Shinto and Buddhism, many Buddhist clergy who had managed jinja through their temples reverted to being lay people, and became Shinto priests to look after the jinja. Most of these were Buddhist monks, but some of them were Buddhist nuns, and they became female priests.
However, with the government decision to make all jinja into government agencies and staff them all with civil servants, this created a problem, because civil servants had to be male. (Overt sexism in the nineteenth century should not really be a surprise.) There was, I believe, no strong action taken against the existing female priests, but women could no longer become priests. Thus, female priests naturally disappeared.
There was a significant movement within Shinto that opposed this, and campaigned for the government to allow female priests. Indeed, the fortunes (omikuji) found at most jinja and temples in Japan were popularised in their current form by an organisation that campaigned for the recognition of female priests; they sold the fortunes to jinja and temples to raise funds for their campaigning. The government had still not been persuaded when the war ended, and Shinto was abruptly cut loose from the state.
Almost immediately, the newly established Jinja Honchō recognised female priests. At its foundation in 1946, the regulations did say that priests had to be male, but that was interpreted as only applying to chief priests; the first record of a female priest in the modern era is from September 1946. In 1949, the regulations were formally changed to allow women to become chief priests as well. There are no records of serious controversy over this change, which suggests that it was not, in fact, controversial.
Today, around 40% of people training for the Shinto priesthood at university are female, and the number of active female priests is climbing, although it is still around 10%. It is important to remember that the average career of a Shinto priest is somewhere around 60 years; it takes a long time for things to change. Indeed, Shinto would appear to be a good example of just how long it can take. There is no fundamental opposition to female priests, and no evidence that there ever has been. However, the simple fact that priests were almost all male has meant that now, 70 years after women were allowed to become priests, they still only make up 10%.
I do hope to see the first female president of Jinja Honchō in my lifetime, but I am not confident. I am not aware of anyone in my generation in a position to be a serious candidate for the position, and since presidents of Jinja Honchō tend to be over 65, I will have to stay healthy if I am to be around to see it. Still, my knowledge of female priests is not encyclopaedic, so I might be lucky.
It is, perhaps, unsurprising that a practice explicitly devoted to preserving traditions as they have been handed down is slow to change, even when the practitioners have no objection to the content of the change. It is, however, something to bear in mind when hoping for transformation within Shinto.