Facts are not her language. She looks at a rainbow and says, "That's beautiful." You say, "It's created when light refracts through drops of water. The light is split..." She says, "But it's beautiful."
You have to connect with her on her level - largely emotional. But that doesn't mean you can't bolster an emotion with facts. Lead with the emotion, follow with facts You lead with facts, you're done.
It's more important to understand her way of thinking that trying to change her mind about something. Read The True Believer by Eric Hoffer. It is an excellent treatise on social mass movements, their causes, endings, and the structure of them. They are largely made up of a group of people who are searching for meaning in their life (the frustrated). When they find a cause that they feel gives them a higher purpose, they latch on to it - feeling they are part of something "bigger than themselves." The leaders of the causes are generally fanatics who spend most of their time convincing the frustrated their cause is meaningful and worthwhile. All the while , leadership is co-opting their minds and pocket books. The cause can never be solved, else it dies. Usually, the cause is given immortality by making the goal of the cause un-achievable: world peace, economic equality, social equality, a chicken in every pot, public lands in public hands - pick your poison - they are ALL causes without end...think about that.
Also, her life's filter does not prioritize things the same way you do. Read Jonathan Haidt to understand this concept.
So, what to do about your sister-in-law...don't tell her a damn thing...ask her so many specific questions as to what she is interested in until it exhausts her knowledge. Ask her what her specific goal is and how she is achieving it. Ask her how much money and time she donates, etc. When she runs out of valid information, she'll feel like you've listened, and then you can tell her what you and the organizations you belong to have done. And validate her concern - you'll never change a closed mind. Commonalities keep minds open - remember that. Find something you agree on, then work from there.
I know a bit of what I speak...I gave a lecture at the University of Washington on elephant hunting- yes, elephant hunting. It was for an interview class and as part, I used an interview with an elephant-hunting friend of mine. I used the commonality of the desire for habitat preservation and overall elephant herd health to connect with the listeners, then moved to poaching, then moved to human/elephant conflict, then moved to the living conditions of rural Africans in the Mbiri district in Zimbabwe. I made a lot of anti-elephant hunting people in to pro "as long as it helps overall" people. And that was good enough. But I led with emotion, followed with facts. I also made damn sure I knew my stuff - inside and out. It worked.
Good luck.