It would be difficult to think of a less applicable word for Eliot than "feminist." Feminism is a philosophical position, grounded in major theoretical work going back at least to Mary Wollstonecraft: it is not a simplistic notion of very occasional sympathy (intermixed with one of the most misogynist images in all of literature in the Fresca of the Facsimile "Fire Sermon" or the tendency to dismiss women writers with the exception of Marianne Moore and Djuna Barnes for Nightwood or a poem about strangling a woman).
Putting aside even Wollstonecraft and DeBeauvoir and Rich and the courageous women of the Suffrage movement, since The Feminist Mystique, at least, scholars throughout the world have studied the meaning and applications of feminism--the history and analysis is massive now.
None of that is simply an intermittent ability to show potential empathy. And to claim the word, one does need to know what it is.