This raises the question whether feminist is the right word for those definitions. Humanist, maybe?

I'm not trying to "all lives matter" the situation – the history of the treatment of women warrants specific advocacy. But I think of a feminist as someone who (regardless of gender) is actively an advocate for change, not just someone who believes in equality.

That's the connotation I have for the word anyway. Clearly UN Women are a more authoritative source, and they specifically use the word "belief," so my connotation seems to be wrong.