"Women get to do stuff that isn't cooking and cleaning by becoming honorary men, either by ruling or by going to war."

Arwen gives a pretty strong turn when she saves Frodo from the black riders, but I think you're working overly hard with the "honorary men" claim which effectively negates the areas in which women have gained or show equality.

No, there isn't a lot of discussion of cooking and cleaning, nor is there a lot of discussion by men of building bridges or planting crops. As mentioned, not the story Tolkien wanted to tell, with its parallels to World War I. (In which he served.)

Does it reflect modern feminism? Nope.

How could it? Because that didn't exist in the era in which Tolkien grew up, the time in which he wrote the story, or, indeed, in the time in which the story is set.