Plastic packaging has issues but climate change is not one of them. Shipping also isn't impactful at all. Most shipping emissions happen when the product moves to the store, not when it sails in a container ship.

Based on your post, the main evil of the corporations is manipulating the media, confusing people with things like abolishing plastic straws (which are very efficient at what they do).

Eating beef, owning a car and buying unnecessary stuff (for example those bottled drinks) are huge. They easily make up half of a persons emissions. An accurate measure is hard because of secondary effects like needing less road with fewer cars.