Unless you can demonstrate an actual harm that these people are doing to the cause, I am going to give them my support for doing SOMETHING. If it moves the needle a millionth of a percent in the right direction, tear down all the art galleries. We only have one planet.
Many of these cases have had jury nullification, which means a jury of twelve people who have been vetted to remove bias, all unanimously agreed to say "fuck you" to the legal system rather than lock up JSO activists.
That tells me that there is considerable public support for them, whatever you say to the contrary.
Edit: Here's a study about the actual problems facing the climate movement. Support isn't the issue:
https://www.nature.com/articles/s41558-024-01925-3
Abstract:
Mitigating climate change necessitates global cooperation, yet global data on individuals' willingness to act remain scarce. In this study, we conducted a representative survey across 125 countries, interviewing nearly 130,000 individuals. Our findings reveal widespread support for climate action. Notably, 69% of the global population expresses a willingness to contribute 1% of their personal income, 86% endorse pro-climate social norms and 89% demand intensified political action. Countries facing heightened vulnerability to climate change show a particularly high willingness to contribute. Despite these encouraging statistics, we document that the world is in a state of pluralistic ignorance, wherein individuals around the globe systematically underestimate the willingness of their fellow citizens to act. This perception gap, combined with individuals showing conditionally cooperative behaviour, poses challenges to further climate action. Therefore, raising awareness about the broad global support for climate action becomes critically important in promoting a unified response to climate change. Global support and cooperation are necessary for successful climate action. Large-scale representative survey results show that most of the population around the world is willing to support climate action, while a perception gap exists regarding other citizens' intention to act.
The abstract of that paper says that the real problem is people's lack of awareness of how incredibly high the support for climate action is, because that informs how likely they are to act.
In which case, all this hand-wringing about which actions increase or decrease support is a red herring, because the support is not actually in danger.
I would suggest that the real problem is people who handwring about the support creating the perception that the cause is less popular than it is.