The short answer is yes, because palm oil comes from a plant source. There is two parts of the palm oil tree where we get oil from, the fruit and the seed of the fruit. But the method of producing has pushed many animal species including orang-utans, elephants, rhinos and tigers to the brink of extinction.
Palm oil can be found in both food and beauty products. Foods use palm oil which is extracted from the pulp of the fruit, while beauty products uses palm kernel oil from the seed of the fruit.

It is estimated that every hour, that an area the equivalent of 300 football fields are cleared for palm oil production.

You probably don’t notice that palm oil is the most used vegetable oil and is in most packet supermarket items. Sometimes, because of the negativity surrounded by palm oil production, brands label it under different names from very broad names like ‘vegetable oil’ to ‘sodium laureth sulphate’. A full list of names can be found HERE 

Its your decision weather or not you include palm oil in your diet, there are options for sustainable palm oil, their logos

Items Containing Palm Oil

Lipstick

Palm oil helps lipstick apply smoothly and it helps hold colour.

Instant Noodles (Ramen, 2 Minute Noodles etc)

Palm oil is used to pre-cook noodles so that all you need to add is hot water.

Shampoo

Used to restore oils stripped away from most shampoos

Soap

Keeps the skin moisturised while removing dirt.

Sources

wwf.org.au

worldwildlife.org