If someone doesn't care one way or another, the label is useless. If someone has a positive opinion, the label helps the consumer seek it out. If someone has a negative opinion, the label helps the consumer avoid the product. If they fight against labeling it is because they consider that the third group is or can become bigger than the second.
I mean, that's so vague that it can be said about anything: Some people think X is positive and will buy the product and some people think X is negative and won't buy the product. Pretty obvious.
The purpose of food labels is to increase safety, transparency and honesty around the contents of food. Companies who oppose safety, transparency or honesty and/or produce products with questionable contents will oppose labels and companies who support safety, transparency and honesty will support them. I don't know many end-consumers who oppose labels themselves. But they will oppose products that contain questionable ingredients, so transparency is bad for companies that produce those products.