It is understandable that, as you report, many artists and green groups are protesting against arts institutions receiving sponsorship from BP but it is important to describe what such corporate charitable donations are and what they are not. They are not in any way ever a meaningful contributor in a company’s overall obligations to its stakeholders. The amounts are collectively too small and the selection of recipients is far too random for the largesse to be anything than incidental in the context of a big company’s finances.
While some companies might seek to suggest that donations to good causes are part of their commitment to “corporate social responsibility” the public is unlikely to be fooled you cannot buy yourself a good reputation or build brand approval by making such gifts. In reality one of the main reasons that big companies donate to arts institutions is to buy their directors privileged access to events, such as to premium seats at the opera house. For the arts institution it is a harmless and valuable source of funds to pander to the vanities of a few corporate fat cats. No wonder they are rallying round BP at the moment.