Nothing to do with feminism in this context.

Now this made me think. I agree that some mfg spend could be construed as unethical. But not the collecting of points and miles by taking up a public offer that is a method of gaining a profitable customer in the future. Surely one keeps at least some of these credit cards because they do turn out to be valuable beyond the first year. I know I do more than I anticipated.
Sorry to say that in my opinion your SO is misguided and you will be better off in the long run canceling her after the fee-free period and going with someone more in sync with your mindset.