Rupert Read has an article at Aeon on climate-related civil disobedience. Its argument is somewhat difficult to follow because Read is never very precise about what one would be disobeying, but it also, I think, shows some sloppiness in Read's understanding of civil disobedience:
The classic philosophical debate around civil disobedience (or nonviolent direct action) asks: is there a right to engage in this form of conscientious law-breaking, under circumstances of deep wrong, where conventional methods of addressing that wrong have failed or are unavailable? It’s widely accepted among philosophers that there is such a right: it is virtually unknown for philosophers to argue against it; even an extremely mainstream liberal individualist such as John Rawls argues for it. And the climate crisis fits the bill for the exercise of this right. Because it is a case of a huge and urgent injustice – a threat to the very viability of ongoing human civilisation, an existential risk – where conventional methods have been tried and failed, and moreover where vulnerable unborn future generations are not able to stick up (let alone vote) for themselves to try to redress the matter.
All of this is an argument that there is no need to debate this particular matter, which is "basically settled". It is, I think, clear that appeal to "vulnerable unborn future generations" is not anything about which anything has been "basically settled at all"; this, despite the fact that I probably have a view closer on this particular to Read's than most philosophers. But, that aside, Read seems to misconceive the role of injustice in civil disobedience. The two (relatively) uncontroversial rights to engage in civil disobedience are (1) when a law requires you, yourself, to do something morally wrong and (2) when a law is inconsistent with your specific rights and responsibilities as a citizen. Anything beyond these is certainly controversial, regardless of the injustice in question, and, indeed, has to be, because of the 'civil' part of 'civil disobedience', which essentially means 'as a citizen'. If you disobey a law, it doesn't matter what injustice you claim is associated with it; you aren't engaging in civil disobedience unless you are doing so in your capacity as a citizen. In a case where this is not so, disobedience could, perhaps, still be justifiable -- that is itself controversial -- but it wouldn't be civil disobedience.
Marchers in Birmingham, for instance, were specifically trying to call attention to provable violations of the rights of citizens in Birmingham, and the law they specifically disobeyed -- the law governing parade permits -- was being deployed to prevent the exercise of their freedom of assembly and speech, by being used in such a way as specifically to prevent them from calling attention to the violations. The protest was also, as Martin Luther King, Jr., noted in the "Letter from a Birmingham Jail", for the explicit purpose of trying to force the city to negotiate over its continued imposition of segregation; also in view (more indirectly and less immediately) was its failure to provide reasonable protection to citizens against the racist domestic terrorism that had earned Birmingham the nickname of "Bombingham". This kind of disobedience is clearly civil disobedience. The whole point was citizenship; the whole action was an attempt to act as citizens; the actions taken were carefully calibrated to leave open alliance and cooperation with other citizens; the whole problem was the failure of the city to take citizenship seriously, and the response was specifically to hold the structures of government responsible to the power of citizens; the intent was at least in part to uphold rights and protections that in the long term would also benefit all citizens, not incidentally, but precisely as citizens.
It is very difficult to fit most climate-oriented disobedience of laws into this kind of model. The laws disobeyed are often not being used specifically to harm anyone's role as a citizen and do not, in themselves or as applied, require anyone themselves to do something unjust; the injustice to which activists point is often diffuse and not specifically tied to citizenship; the actions are often not defending citizens against government action but bullying other citizens. To the extent that these are the case, one can call into question how much the disobedience is civil disobedience at all. This is not, of course, to say that civil disobedience is impossible on climate-related topics; but civil disobedience is an action of citizens, as citizens, on behalf of all citizens, and something can only be justified as civil disobedience to the extent that it is so.