This is a time when the Royal Institute could refuse to let her give a talk simply on the grounds that she was a woman.
I find that extraordinarily hard to believe. Can you produce an actual quote wherein the Royal institute gave that reason?
It would be as suicidal to give that reason then, as it would be now.
Of course, in practice, people do tend to quietly assume that women tend to be idiots in certain fields, and might well not allow one to speak for that reason, but they don't say the reason out loud in plain words.
I don't have an actual quote from the Royal Institution, and I doubt that they specifically gave that as a reason in this particular case. This page from the American Institute of Physics biography says that "custom ruled out women lecturers". I concede that this might be a myth, but I don't think your skepticism is justified. The claim that this sort of reason would be as suicidal then as it is now is, I think, patently false. That sort of discrimination, often justified on the grounds of tradition, was pretty common in the early 20th century.
T...
Today is Ada Lovelace Day, when STEM enthusiasts highlight the work of modern and historical women scientists, engineers, and mathematicians. If you run a blog, you may want to participate by posting about a woman in a STEM field whom you admire. But I'd love to have people share women scientists/mathematicians/authors in the comments that they think we could all stand to read more about.