Even when people agree on the problem, differing opinions lead people to support different solutions to the problem.
Every movement has its fundamentalists, but not everyone of that movement is a fundamentalist. Some people take a more compromising stance than others.
Your question is implying that the anti-public-transport climate activists are shooting themselves in the foot. Regardless of whether that's correct, you could find similar "shooting in the foot" arguments in pretty much every movement or philosophy, which is usually biased towards things the observer personally disagree with.
Note that the examples I use here are purely demonstrative and while I try to avoid bias, I'm not perfect either. I'm not labeling anything as good or bad, I'm merely pointing out its existence.
You have vegetarians who don't eat meat in order to avoid animal suffering, but some anti-animal-suffering activists argue that farm animals used (for purposes other than eating) are also a form of animal suffering, e.g. having cows/horses pull a plough. Arguably, this can be seen as the same "shooting in the foot" principle as the one you're highlighting, as it hinders the growing of plant-based food (which would be needed to replace meat in an omnivoruous diet).
Similarly, you have anti-discrimination activists who advocate equality; but some activists have argued solutions that are tantamount to discriminating the other way, in an attempt to counterbalance the system. This again arguably can be interpreted to shoot the original intention in the foot by perpetuating discrimination, but simply redirecting it at other people.
I don't think I need to elaborate on religious examples here but the principle is the same there too, not everyone draws their line the same way. Some people read their scriptures more literally than others, which is exactly why different movements can exist within the same encompassing religion.
Regardless of me agreeing or disagreeing with any of these stances (believe me when I say I've picked both things I agree and disagree with), it's unavoidable that some people take an above average hardline stance, whereas others take a below average "softline" stance (by semantical definition of what an average is). I'll use your climate activists as an example. The general idea can be summed up as (oversimplified):
We should stop manmade climate change. Emissions from transportation are one big example of something that causes manmade climate change.
But different humans find different solution to the problem. There are myriad approaches possible, but I'll specifically focus on a few that are relevant to your question:
- We should lower car usage as this will lower emissions. Public transport emits notably less pollution (per person) than personal vehicles.
- We should ban all motor vehicles, as this will lower emissions.
- We should get the government to take action against climate change, as this will lower emissions. We should protest and use civil disobedience to get the government's attention.
Three different opinions, all intended to lower emissions, all with sound reasoning. But three wildly different approaches which conflict with each other (e.g. you can't shift people towards public transport and oppose public transport at the same time)
Your stance is the first one. The people who disrupted public transport fall into either the second or third stance (or any other stances I may have omitted).
I'm not interested in picking who's wrong and who's right, I'm just pointing out that even when people agree on the problem, they might still back different solutions to that problem.