1.) You will NEVER unite enough people to actually pull this off.
2.) IF you were able to actually pull this off then what would occur is:
(first let's clarify how OLD this email is: Exxon and Mobil are not the 2 largest, they MERGED they are the single largest)

If everyone stopped buying from ExxonMobil the demand on other refiners would exceed capacity. THEN they would contract ExxonMobil who now has PLENTY of capacity (because you are not buying from them) to produce the balance needed to meet the demand. NOW you are boycotting ExxonMobil and buying ExxonMobil's gasoline at Shell, Chevron, etc. Only thing you did was to KILL the individual station owners who are trying to put their kids through college.

The refiners in the USA often contract to other refiners to help meet production if they can't, it happens everyday. When the cost of a barrel of oil is $100+ it does not matter who refines it, the end product price goes up. Want cheaper oil prices? Stop protecting the OPEC nations who are dictating the price of oil. We are spending BILLIONS to protect middle east oil producing nations, they in turn rip off not only us but the world. Add to that China is consuming more and more causing the demand to push supplies to the limit and you know what happens when supply runs low. Prices go up. The problem far too complex for a simple solution as you propose. It's more like buy a bicycle or bust OPEC, either one is going to he a huge effort on our part.

(I'm retired-fuels production supervisor ExxonMobil)