Most of the time on the internet (or at least the parts I visit) if someone is talking about essentialism it's gender essentialism. I'm not going to talk about that specifically, but rather I'll talk about an essay by Ernst Mayr on essentialism that I read in the Oxford book of Modern Science Writing.
So what is essentialism? It goes back to the ancient greeks, especially their geometers who made a lot of progress by recognizing when two dissimilar looking things are really the same thing: for example all triangles are really triangles, even if they have different angles or lengths of sides. A triangle is not a rectangle, you can't have something that is part rectangle, part triangle. This is undeniably true in math, but Plato expanded the idea out to everything: everything is just a reflection of an "ideal". In this way of thinking not only were all triangles totally separate from rectangles, but all birds were totally separate from all reptiles, and it was just part of their natures that could not be changed.
Mayr in the essay argues that this held back biology, because everyone was thinking essentially, when biology is nothing like that. I don't know if this is particularly true, many people seemed willing to give up essentialism in biology once there was good evidence against essentialism (the fossil record and such). My point here isn't to argue with Mayr, but rather to jump off and talk about what it would mean if life was essentialist, and I'm going to talk about particle physics, because all fundamental particles really are identical.
Now once you have things that are really, truly, identical like fundamental particles you start running into all sorts of problems. The first one is how do you tell them apart. If they are identical and they get close to each other and you look away when they would hit each other (or not) how do you tell which is which? It is possible in principle in classical physics because every particle has a unique trajectory, and you can (at least in principle) predict it, and use that to tell them apart. Basically you can tell them apart my their positions in space and time. This becomes impossible in quantum mechanics because the particles do not have distinct positions, but rather wave functions. Basically there are two ways of dealing with this problem: the particles can either not ever get near each other (physicsts call these types of particles fermions), or they can bunch up into one particle (these are bosons). The reason we don't see these sorts of things happening is that everything we ever encounter in everyday life is made up of incredibly large number of particles.
What does this have to do with life? Other than illustrating why we would not expect essentalist explanations of incredibly complex things like life (even the simplest bacteria are impossible to simulate based on physics), it shows the problems with essentialism if you really start thinking about it: if everything is only a reflection of an ideal, then where do the differences between similar things come from?