I am not an expert and I cannot understand why essentialism is incompatible with naturalism? Why scientific laws cannot describe essential properties of objects?
Essentialism is compatible with naturalism, Aristotle, the father of essentialism, is typically named as a precursor of naturalism (and even empiricism), and today we have scientific essentialism founded by Kripke and Putnam. Essentialism is simply the claim that objects have some properties "of necessity" while others are "accidental". It usually requires some sort of modal ontology to account for non-actual variations that separate the essential from the accidental, Aristotle's potentialities or Leibniz's possible worlds. This makes it unattractive to empiricists suspicious of metaphysical excesses, for them the way to account for necessity is to make it into a linguistic artifact, necessity by explicit or implicit stipulation. This is called de dicto ("by speech") necessity. But metaphysical minimalism is not essential (pardon the pun) to naturalism/empiricism, although the distaste for metaphysics of possible worlds is shared more widely, and alternatives have been developed, see Is there modal logic without possible worlds?
Historically, the modern controversy over essentialism is linked with the controversy over the modal logic, Tuboly's Quine and Quantified Modal Logic is a nice review. Quine was concerned that one can not substitute descriptions or quantify into modal contexts under de dicto necessity, they are "opaque". It is necessary that 9 is greater than 7, but it is not necessary that the number of planets in the Solar System is greater than 7, even though 9 is the number of planets in the Solar System (well, it was, Pluto was still in). In Reference and Modality he concluded that essentialism is just what one needs to take care of this. Modal contexts are not opaque as long as the descriptions involved are essential, and for 9 being the number of planets in the Solar System is not:
"The Aristotelian notion of essence was the forerunner, no doubt, of the modern notion of intension or meaning. For Aristotle it was essential in men to be rational, accidental to be two-legged... An object, of itself and by whatever name or none, must be seen as having some of its traits necessarily and others contingently, despite the fact that the latter traits follow just as analytically from some ways of specifying the object as the former traits do from other ways of specifying it. In fact, we can see pretty directly that any quantified modal logic is bound to show such favoritism among the traits of an object...
Essentialism is abruptly at variance with the idea, favored by Carnap, Lewis, and others, of explaining necessity by analyticity. For the appeal to analyticity can pretend to distinguish essential and accidental traits of an object only relative to how the object is specified, not absolutely. Yet, the champion of quantified modal logic must settle for essentialism... To defend Aristotelian essentialism, however, is not part of my plan. Such a philosophy is as unreasonable by my lights as it is by Carnap’s or Lewis’s. And in conclusion I say, as Carnap and Lewis have not: so much the worse for quantified modal logic."
Ironically, the subsequent acceptance of quantified modal logic proceeded according to the very plan dismissed by Quine. Kripke explicitly adopted a form of Aristotelian essentialism in Naming and Necessity and made it more palatable, the resulting type of necessity is now termed de re ("by things"), Kripke's version of it "metaphysical".
Why was it unacceptable to Carnap, Lewis and Quine? Because they espoused a particular version of naturalism/empiricism, one committed to ontology of first order languages, where only objects are accorded existence. Properties and relations are treated nominalistically, as mere linguistic predicates. This move is known as semantic ascent. According to Quine's criterion of ontological commitment, "to be is to be a value of a bound variable", and in first order languages one can not quantify over predicates. Hence they are not, and neither are de re essences. And if de re necessity is rejected quantified modal logic is indeed so much the worse.