Besalel’s point has to do with each movement having to portray one way to their community and a different face to the other immunity. The women he mentioned give hashkafa/chaizzuk on the right, which is not much different than pulpit/pastoral roles on the left.
I’m aware that this could be pickled apart. But please give it an extra minute of thought. It is theoretically possible for one woman to do the same thing in two different communities, and it can result in two completely different titles.
Any observant group that has a disagreement with another observant group, will find the same disallowed cause in abundance within their own ranks. We just give it the appropriate label. And complain that a totally different community has different titles for a similar role or idea.