It's quite sound even though you don't understand…
A business sells multiple products. Business phases out products that consumers don't support over time even if consumers continue to buy other ones of the business's products. Happens all the time with numerous business..
As to "If you support any part of something you hate, in effect you support the whole thing.", that just doesn't work in the real world that is inhabited by complex political systems, businesses, entities, etc.
Must society ban all individuals who have any bad qualities, and allow only the perfect individuals to exist?
Do you live in a political society that does everything perfectly to your liking and support; or do you live by yourself on an island or cave, making and carrying out only right and perfect actions every minute of every day?
A family has some members you love and some you hate. Must you shun those you love because of your hatred or dislike for other family members?
Maybe you've never heard about taking the bad with the good and vice versa. Maybe you live in a binary society of good only and bad only humans.
Et cetera…