Your original statement was

Those that just vandalize random art or monuments that have nothing to do with climate change can fuck right off.

From the links you supplied, in two of the three cases (Stonehenge and Flowers) no damage was done. In the case of Stonehenge, the protestors chose a marker that wouldn't damage the monument. For Flowers, I'd assume they knew about the glass. But that's me giving them credit.

For the third (Warhol's soup), damage was done but remediated.

The protestors are being unfairly accused of fucking up art without justification. Others have used that to dismiss the protests and the cause, which is bullshit.

The protestors have a good cause, they're getting people to (at least) talk about climate change, and they're taking the punishment for their actions.

It has been clear for decades that governments should act quickly, wisely and decisively, but they simply do not, preferring to look for other issues. The kids from Just Stop Oil poured soup on glass and sprayed chalk on stones to draw attention to the huge emergency that we collectively ignore. They wanted to attract attention, and they succeeded. But their fellow human beings don't want to think about the impending climate collapse, let alone take action and join an active protest. That would require leaving the comfort zone. So they get upset anonymously on the internet about the form of protest and act as if art vandalism was being practiced here.
Cognitive dissonance is when your convictions do not match your actions. You solve it by changing either your actions or your beliefs.