We can’t stop looking at human faces. Can’t stop being interested in ourselves, our species. The BP Portrait Award, whose annual exhibition of winners and strong contenders can be seen at the National Portrait Gallery until 24 September, is full of humanity. It is, perhaps, the most humanist art prize in the world, an art award that specifically celebrates the painted human image and looks for modern heirs to the profoundly compassionate tradition of portraiture that includes Rembrandt, Velázquez and Lucian Freud.

Yet it may be time to get over ourselves. Has the moment come to put nature before portraiture, and abolish this oil-tainted oil painting prize?

Protests against BP, probably the world’s most reviled oil company since the Deepwater Horizon disaster in 2010, are regularly staged outside its annual prize giving ceremony. Now the pressure is being ramped up a notch.

For the first time, the Guardian has learned, a winning artist is rejecting part of BP’s prize money. Henry Christian-Slane, 26, from New Zealand, won this year’s BP young artist award, one of five prizes in the open submission contest. He’s donating £1,000 of the £7,000 he received to Greenpeace, to support “projects that aim to protest BPs further extraction of fossil fuels from the Earth”.

Christian-Slane is not calling for the end of this art prize – that would be a bit hypocritical, having entered it – yet his gesture undoubtedly turns a harsh spotlight on the BP Portrait Award’s oil funding at a time when BP arts patronage is under attack. Tate’s relationship with the oil and gas extractor has ended (for non-climate related reasons, insists BP) and some say the writing could be on the wall for other arts organisations accepting its sponsorship.

I should probably declare an interest. I accepted an invitation to be on the BP Portrait Award jury a few years ago . I did not get paid anything, but I did have a nice dinner and happily sat on the judging panel of six with a voting BP representative. Since our arguments got quite heated, her vote mattered.

It is sometimes argued that BP arts sponsorship is a fake publicity stunt that museums can easily do without – after a long relationship with Tate it turned out BP’s annual spend across its galleries averaged less than £250,000 – but if that is the rule, the BP Portrait Award may well be an exception. It isn’t so much the money – no doubt that is peanuts for BP – as the quirkiness and originality of this particular prize that makes the oil company’s involvement look almost – I hate to say this – idealistic.

Painted portraiture is, after all, not exactly a fashionable art form. None of the people who enter this prize are ever likely to be shortlisted for the more stylish Turner – I’ve judged that too and can attest that the chances of a portraitist winning it are close to zero.

Painting people well is hard, and in the cooler regions of the art world, unrewarding – yet in spite of that, so much of the truly great art of our time, such as Freud’s portraits of Leigh Bowery and Sue Tilley, has come from cussed sods who do it anyway. Freud worked all his life to get that good. I can’t help being grateful to BP for giving a bit of its dosh to Christian-Slane for his sensitive and promising painting Gabi. It is young painters like him who may become the Freuds of the future – and frankly they do not get much encouragement or fame outside this art prize.

Then again, how much do portraits matter? How much does art itself matter? I think the debate about BP sponsorship of the arts is dishonest if it does not ask these bigger questions. It’s all very well bullying art galleries – that are struggling, not just to survive in a harsh economic climate but to stay free as the British public expects – to divest themselves of BP support.

The reality is that if we’re making it harder for the arts, we should be prepared to say some things matter more than art. And they do.

One of the Greenpeace campaigns that will benefit from Christian-Slane’s cash is its effort to save a newly discovered coral reef at the mouth of the Amazon. This 600 mile reef, which was a kind of scientific legend, an oceanographic rumour, was proven to exist by Greenpeace itself in 2016. The images taken from its submersible are wonderlands of colour and abundance – a beauty no artist created.

This is, however, a beauty that humans can easily destroy. And guess what: BP is one of the oil companies targeting the area. It says it “expects to begin exploratory drilling operations before August 2018”. It claims that its operation about 22 miles from the magical corals and their denizens will be completely safe. Uh-huh.

Looking at the wonder of this unique reef – it exists in exactly the kind of murky waters that are not meant to support corals – it is impossible for me to claim a painting matters as much. As the great, campaigning Victorian art critic John Ruskin pointed out, human art can never hope to match the grandeur of nature. The sky is brighter than any painting, the sea – as we can observe in images of this reef – more mysterious than any human fantasy. Without nature there can be no art. It is blind and narrow for arts organisations to pretend they are outside the struggle to save nature.

So make this a turning point. A young artist has bitten the oily hand that feeds the BP Portrait Award and he’s surely started something. If artists don’t want BP’s money how can the National Portrait Gallery keep offering it? Tellingly, the first sponsor of this prize was the John Player and Sons tobacco company.

It seems it’s always the controversial businesses that spend on the arts – the saintly ones don’t crave the publicity. Today it would be unimaginable for museums to take tobacco money. Perhaps museums need to find the next sponsors who need to clean up a dodgy image – soft drinks giants, maybe?

It is not true that you can cut off a source of money to museums without harming art. Without BP there might be no portrait award. So let’s tell it truthfully: in the interest of the planet, art will just have to lose face.