People definitely argue about the canon and do draw up lists well before Trent; I'm not sure it was 'organic', since it was certainly formalized.
I can see the links between people (men) declaring they have authority to decide which bits go into the Bible and people in this CU decide women don't get to teach, since it's all a bit circular, but I tend to assume (maybe wrongly?) that this sort of CU is probably less about revisiting old theological controversies and more about finding a way to justify 'traditional gender roles' which they're assuming are therefore scriptural. I could be being unfair.
It just seems that a fair few Christian groups seem to imagine the Bible must promote the kind of gender roles the 21st century celebrates as 'traditional' (ie., 1950s-that-never-were) and don't really bother to check it out properly.