Royal Dutch Shell (Shell Oil) has five core businesses: Exploration and Production, Oil Products, Downstream Gas and Power, Chemicals and Renewables. Due to regulations that came into effect during the antitrust breakup of Standard Oil Company, it became against the rules for companies that do exploration to exclude competing refineries from purchasing their crude oil and for the refineries to exclude competing marketers from buying their products. (This is how we get PC brand engine oil.) A large portion of the price of gas is actually taxes, and a boycott of votes for a certain political party would do more to affect the provincial taxes than a boycott of certain gas franchises,
If people stop buying gasoline from Shell service stations, the refineries will just sell more gas to the other marketers. Imagine the exploration guys from every company putting all their crude into a giant pool. Then imagine the refineries buying the crude to refine, refining it and putting it into another large pool. The service stations then buy the refined products to sell to the consumer.
A boycott would mean that Royal Dutch Shell loses gasoline sales, but they also lose the cost of buying the gasoline from the pool in reality this means a relitivly small drop to the bottom line. Lost Big Gulp sales probably hurt them more.
Another thing that people have seem to have forgotten is that if everyone stops buying gas from one or two stations, what would prevent the other stations from raising their prices even more because of the new found demand. If I were a regional manager, that suddenly didn't have to compete with Shell or Esso I would raise my price while I could. Especially if I couldn't get oil delivered fast enough to compensate for the increase in demand at my store.
More competetion is better for the consumer than less. Don't force less competition on yourself by boycotting gas stations. Force lower gasoline taxes by changing government.