Most "equivalent generics" are in fact made by the same companies that make the major name brands, in the same factories; they cost less because lower marketing expenses.
If you buy store generic-equivalents, its quite likely your money is going to exactly the same major corporation as the name brand in pretty much the same quantity (after deducting that the part that the major corporation would be paying to marketing/advertising firms to market the name brand.)
So, while it saves you money, it may not be as effective a boycott technique as you think. Unless your boycott target is the advertising industry.