The ‘Become Ocean' performance is being put on at the Perth International Arts Festival, performed by the Western Australian Youth Orchestra, and the WA Symphony Orchestra, both of which are sponsored by Woodside.
Composer John Luther Adams described the piece as being about "the prospect that once again we may literally become ocean".
Activist group Fossil Free Arts WA wrote to the boards of WAYO and WASO requesting a meeting to discuss their concerns, but were denied.
Woodside CEO Meg O'Neill sits on the board of WASO alongside company chairman Richard Goyder.
The letter said it was ironic that a Perth Festival performance about climate change is being sponsored by a fossil fuel company that is actively contributing to rising global temperatures.
Woodside sponsors a number of community, arts and entertainment programs across its home state, including the Fremantle Dockers football team and the WA Ballet Company. Former CFO Sherry Duhe was on the board of the latter, also.
It has faced a sustained campaign by climate and environmental activist groups which describe its involvements in such programs as attempts to maintain social licence that amount to greenwashing.
"There's a real hypocrisy when you program a concert about celebrating the ocean while promoting a company such as Woodside who are actively trying to destroy it with their disastrous and criminal Scarborough Gas Hub," Fossil Fuel Arts spokesperson Madeleine Antoine said.
A Woodside spokesperson told The Guardian its partnership deal with WASO was "helping develop our local talent, creating pathways for the next generation of gifted musicians".
"Through the partnership, WAYO musicians are provided with unique opportunities to learn from Western Australia's professional state orchestra," she said.
Previously Woodside was forced to drop its sponsorship of the Perth Fringe Festival after attracting criticism from participating artists. Woodside later diverted its funding to Artrage - the company which runs the Fringe event - rather than the festival itself.
It also received criticism for sponsoring the WA Surf Life Saving's Nippers program, dubbed "Woodside Nippers".
Funding of the arts by oil and gas companies has been attacked in Australia and overseas. The Royal Shakespeare Company ended its partnership with BP in 2019 after sustained criticism from environmental groups.
Earlier this year Tennis Australia announced it had ended its contract with Santos as its "official natural gas partner", however it was unclear as to whether this was due to social licence concerns.