Not everyone in a family has to have the same worldviews. Just look at Elon Musks daughter for an example of this.

Hey if I found out my family fortune came from the slave trade I'd work against that. I imagine finding out your family's fortune came from the petroleum industry is pretty depressing when you look at our world - knowing that you profited on all this misery and loads more misery to come. Better to get out ahead of it, whether subconsciously or deliberately.

The most cynical view is that she funds them specifically because it makes climate protestors look bad. They are radical in their methods and their targets seem to just be random spaces where there is a larger(but not too large) public density.

However the reality is probably more complicated. She might disagree with her grandfather and agree with their message, she might think that pulling funding would be worse PR than the few headlines that JSO generates, or she might not care one way or the other.

She has no financial interest in the fossil fuel industry. At all.

It is well documented that she is acting out of remorse over what happened and is trying to make things right. Again: She does not benefit from the fossil fuel industry at all. The story that she is a covert operative working for the fossil fuel industry has been debunked time and again. Stop the conspiracy stuff

I can see it from a guilt perspective

I'll believe they are a psyop. Either that or they got some insane feedback loop in their circles leading them to believe this stuff actually helps.