Unite said its members at the Ineos site in Grangemouth, backed action short of a strike by 90%, with 81% saying they would support stoppages.
The dispute centres on union official Stevie Deans, who was involved in the bitter row with Labour over the selection of a candidate in the Falkirk constituency.
Mr Deans, chairman of the constituency party, faces an investigation by Ineos over issues linked to the row.
Unite Scottish regional secretary Pat Rafferty said: "This overwhelming result reflects the genuine ill-feeling held by the Grangemouth workforce because of the grossly unfair treatment of Stephen Deans, who has 24 years of loyal service at the site. This tight-knit community has no tolerance for the unfair treatment of a trade unionist because they know that an attack against one is an attack against all."
The AA said a strike should not impact on motorists as the industry was well-prepared. A spokesman said: "The fuel industry is very adept at moving fuel supplies around the country. Usually the threat of disruption is worse than the reality."
Calum MacLean, chairman of Ineos Petrochemicals, said: "There cannot be one rule for union officials and one rule for everyone else. "