What picture exactly is of course not important. Any popular picture with a glass plate in front of it could have done the job. I don't they have any ax to grind about Vermeer, nor will the controversy have any connections to him or his art.
I don't think this is true, for most people. People do not generally stop and think in a deep and reflective way after getting angry about something. What these activists did was not inspiring and it did not look like justice. They aren't Rosa Parks 2.0, they're people throwing liquid at inanimate objects (which people beautiful and valuable) and gluing themselves to objects at a museum. There is no powerful symbolism of defiance here, this is not speaking truth to power. They just look like childish weirdos. Childish weirdos do not make me self-reflect and question if I'm actually the one doing something wrong.
This is correct. The target is an irreplaceable piece of art. It's supposed to stand in for the earth (or some subset like nature). That's the point. The stand-in for the petroleum industry is whatever commodity they are throwing at it
It's also pretty logical because it doesn't actually cause permanent damage, but sensationalist headline writers make it seems like it did. So the stories get more virality then they otherwise would.
The reason why this doesn't look rational or 'for the cause' is because the target in question really has nothing to do with the petroleum industry. Johannes Vermeer painted this art in 1665 before the industrial revolution. The subject is just a woman with a pearl earring. So neither the painter nor the work of art have any persuasion or symbolism that encourages fossil fuel use. It seems totally illogical to commit an act such as this. I think the public at large sees no connection between what the activists went after and what they are trying to achieve. When that happens, it delegitimizes the movement in peoples eyes.