Role of women in LOTR

[Tuor of Gondolin]

I didn't find anything related to this topic in a search of threads of several years, so:

How is Tolkien's treatment of, and the roles of, women in Middle-earth viewed by readers? Is it perhaps sexist? Has the perception changed by readers since the 1950s, and if so, is that an unfair critique. Given the general "heroic age" of the saga and that it was written in the first half of the 20th Century by a generally conservative in philosophy writer, it could be argued that women in such a society are represented adequately. One observation I saw elsewhere pointed out the tendency in modern film (and book?) stories to have women act essentially as men (see Xena et. al.) Galadriel and Goldberry wield a different kind of "power" then simple swordplay. And the one who fights like a warrior does so with considerable reason and is a much more interesting and sympathetic personality than portraying women fighters as almost androgynous.

Eowyn to Aragorn:
"All your words are but to say: you are a woman, and your part is in the house. But when the men have died in battle and honour, you have leave to be burned in the house, for the men will need it no more. But I am of the house of Eorl and not a serving-woman. I can ride and wield blade, and I do not fear either pain or death."