After a visit to the National Zoo and Aquarium we have vetoed products in and around the home that are produced by companies/organisations that farm unsustainable palm oil. To name a few things, I've changed my brand of shampoo and conditioner, moisturiser, make up, deodorant, coffee, oil, cheese (and other dairy products). Whilst the product that you are buying may not contain palm oil, the parent company may be using it in other products.
The Taronga Conservation Society has a lot of information on palm oil.
To help me in my shopping I've downloaded the Shop Ethical android app. There are lots of things that we no longer buy that used to be family favourites.
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