Well, it depends. Let's do a little elementary taxonomy lesson before I tell you about my personal experience.
All living things are grouped into categories. This method of grouping is called taxonomy.
When we talk about foods and anything that grows, it is all in the plant kingdom (plantae). There are a zillion different kinds of plants, and out of those there are tons that we eat. Botatnists can map them out into smaller and smaller groups depending on their genetic makeup.
For example, you may have heard that potatoes, eggplant, and tomatoes are all in the nightshade family (Solanaceae). It is extremely rare to be allergic to all nightshades. (As an unrelated side note, nightshade intolerance is more common.)
Different tree nuts are all in the same family and class, but are different orders. Yet, busy allergists commonly mix all the nuts together into "tree nuts" and tell patients to avoid all of them. People who are allergic to one tree nut are very commonly allergic to one or more others.
Palm is a family called Arecaceae. Try spelling that without looking! Coconut is in this palm family along with things like date palms, which are in a different genus.
Let's now compare Coconut (Cocos Nucifera) vs. Babassu (Attalea Speciosa). They are not only in the same order, but are in the same subfamily and tribe, which aren't shown on my chart but are specific subcategories that come before genus. Babassu is basically coconut's closest plant relative.
|Cocos Nucifera (Coconut) is in the center, Attalea Speciosa (Babassu) is right above it!
I have been sent several samples by three different unrelated companies to try products with babassu oil. Two of them claim "coconut free!" on their websites. However, I have had powerful allergic reactions to them every time. However, I do not have reactions to many products containing palm oil, which is also in the same genus and tribe. Palm oil is tricky because it can be sourced from all different kinds of palms. I have occasionally reacted if I eat a product with a lot of it. I would never attempt to eat hearts of palm. No thank you.
YES, if you are allergic to coconut you will most likely be allergic to babassu.
It is somewhat likely you will react to palm.
It is unlikely that you will be allergic to dates.
You absolutely should not be allergic to pineapple unless it's an unrelated allergy.
I welcome feedback from people who are actual botanists, of course! My knowledge of nomenclature is admittedly primitive.