Tell salespeople to hold the bag when shopping. Then put your purchases in a backpack, tote bag, string bag or whatever is your bag. You'll save money and help the earth. Resist buying faddish clothing that will go out of style before it wears out. That's a waste of your money and the earth's resources.
Animals are part of our environment too.
Avoid lotions and perfumes made form animal by-products. This is a pretty long list. No one expects you to be able to do it all. Even if you choose to make just one of the changes suggested here, you'd be helping the earth more than you realize.