Mother-of-two, Tahlia Stolarksi sprayed yellow paint bearing the oil and gas giant's logo across multiple doors at the front entrance of parliament in West Perth on Tuesday morning.
The Disrupt Burrup Hub campaigner demanded a halt to further industry on the Burrup Peninsula, where Woodside operates its oil and gas fields, with expansion underway.
The area is also home to sacred rock art at Murujuga, containing one of the largest and oldest collections of rock art in the world.
Mr Albanese and cabinet ministers are in Port Hedland for regional cabinet, with WA Premier Mark McGowan.
Ms Stolarksi said the WA government permits Woodside to destroy Aboriginal culture and the climate with toxic emissions from the Burrup Hub.
She labelled WA as having a flagrant disregard for cultural heritage and climate change, conflicting with federal Labor's claims to care about Indigenous culture and Australia's international climate obligations.
"Our government subsidises Woodside's Burrup Hub with tax breaks in exchange for the largest corporate donations in the country," Ms Stolarski said on the steps of parliament.
"While the PM and premier parade around Port Hedland, the Burrup Hub just down the road is spewing out more emissions than any other project in the country.
"No wonder WA's carbon emissions keep climbing when the Burrup Hub alone will emit more than six billion tonnes by 2070 after this government approved its expansion."
Protesters sprayed Woodside's logo on Frederick McCubbin's well known painting Down on his Luck at the Art Gallery of Western Australia last month.
Artist Joana Partyka was charged over the incident.
Police were at WA parliament on Tuesday following the latest incident.
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