It is impossible for consumer to "avoid" BP or any other major oil multinational's products.
If there are BP gas stations, you can avoid those, but still, oil that originates from BP's concessions or pojects is in almost all oil-based products, which is nowadays everything, from computers and pharmaceuticals to cars, various kinds of plastic products, fertilizers etc.
Furthermore, there is no "BP oil" or "Total oil", there are blends that are reference for trade, like West Texas intermediate, Russian REBCO, North Sea Brent Crude, Dubai crude or OPEC reference basket.
The world is unfortunately so globalized that calling to autarchy is technically impossible, with rare exceptions like North Korea (among the last ones, if not the last one, and even they have exchange with Russia, China and Syria...) Furthermore, ownership over oil companies is not national, but "multi" and "over and above" national, with significant percentage of ownership hidden and dubious (investment funds, hidden investors...)