As You Sow announced the vote results May 18.
ExxonMobil Corp. faces a similar resolution at its May 25 shareholder meeting.
Phillips 66, which is a joint owner of resin maker Chevron Phillips Chemical Co. LLC, did not respond to a request for comment, but in a report to shareholders argued against the plan.
The company said its CP Chem unit is making ambitious investments to produce 1 billion pounds of circular polymers by 2030 and is working to reduce plastics environmental pollution.
"Phillips 66 and CP Chem are committed to keeping plastic out of the environment and progressing toward a more circular economy where plastic packaging is reused, recycled or recovered," the company said.
But the green shareholders said that even with those efforts, investments in virgin resin dwarf those in recycled materials.
AYS said that while CP Chem was one of the first virgin resin makers to announce a recycled plastic target, its planned investments in virgin plastics production are still three times its recycled resin target.
"Petrochemical companies that are serious about their commitments to end or combat plastic pollution cannot justify continuous and rapid expansion of virgin plastic production," said Joshua Romo, energy and plastics associate at AYS.
"We hope this majority vote will motivate the company to thoroughly assess its exposure to the single-use plastic supply chain and provide investors with information on how it will decrease transition risk as the world moves away from virgin and single-use plastics," Romo said.
AYS pointed to a report from the Pew Charitable Trusts and Systemiq, "Breaking the Plastic Wave," which said the world could reduce ocean plastic pollution by 80 percent by 2040 by tripling demand for recycled content and reducing virgin plastic demand by one-third.
The potential financial risks for plastics producers is a topic getting more attention from some investors, like those at a conference last year organized by the think tank Planet Tracker.
But investors there also acknowledged complexities in evaluating and measuring plastics impacts, as a packaging executive speaking there warned about strains on the world's forests if packaging shifted to more paper, as the Pew report called for.
Phillips 66, in its comments to shareholders urging a no vote on the AYS plan, pointed to a number of actions, including supporting government mandates for 30 percent recycled content for plastics packaging by 2030.
It also said it had invested in recycling operations, brought a grade of circular polyethylene to commercial markets in the U.S. and was a founding supporter of the industry's $1.5 billion Alliance to End Plastic Waste.
It argued that CP Chem's 2022 sustainability report would address many of the topics raised by As You Sow, including evaluating impacts of future environmental scenarios, increased regulation and substitution of alternative products.
But AYS said it believes the petrochemical industry has not looked enough at financial risks from the economy moving away from virgin polymer use.
"While the plastics industry frequently discusses the need to transition towards a circular economy for plastics, U.S. petrochemical companies have not adequately addressed the necessity for or the potential impacts of an expeditious transition away from virgin plastics," said Conrad MacKerron, senior vice president of AYS.
"In fact, as demonstrated by CP Chem, many major plastic polymer producers are investing in a continuous expansion of virgin plastic production," he said.