I will not be fair, the publication isn't. Why should I?
Because arguing dishonestly makes you look irrational and does their propaganda work for them.
but you are more likely to try to distance yourself from fossil fuel reform movements, and that's all they need you to do to be successful.
Not really. This isn't an effective form of protest or reform. Stunts like this allow articles like this to be written in the first place, but the stunts, even if written of with the highest of praise, are useless. Effective action would involve changing the minds of those who profit from fossil fuels the most and making it unprofitable for them to continue. You don't need to convince people who care about world heritage sites or famous artwork. You need to convince the profiteers of industry and that won't come from an appeal to emotion but from a threat to their financial well-being.
It's also possible to be a person who genuinely cares about classic art and the environment already. And it's also possible to be a poor person with little to no power to influence the fossil fuel industry. Chiding people for not having the privilege of free time and minimal obligations to protest isn't very productive. Again, change needs to happen at the top and it's not going to be achieved through appeals to emotion or coercion via symbolic or actual threats to famous art or sites.