Does the hybridization of sp3d2 type exist? Is the hybridization of $\ce{XeOF4}$ $\mathrm{sp^2}$ rather than $\mathrm{sp^3d^2}$, because the latter type of hybridization does not exist?
Every answer in the Quora thread &quot;How can we find the hybridization of $\ce{XeOF4}$?&quot; concluded that the hybridization of $\ce{XeOF4}$ is $\mathrm{sp^3d^2}$. However, the very last answer posted by Steven Fawl, Professor of Chemistry at Napa Valley College (1985-present) reads: &quot;Where to begin? Let me start here - every answer thus far is wrong! This molecule is not $\mathrm{sp^3d^2}$ hybridized. It is actually $\mathrm{sp^2}$ hybridized and I am going to prove it.&quot; The issue that I have with his post is that it only cites a couple of Wikipedia articles as his sources, and it contradicts every chemistry book that I have read by claiming that $\mathrm{sp^3d}$ and $\mathrm{sp^3d^2}$ hybridizations do not exist. The justification he gives for the latter is the following quote from this Wikipedia article:

In 1990, Magnusson published a seminal work definitively excluding the role of $\mathrm{d}$-orbital hybridization in bonding in hypervalent compounds of second-row (period 3) elements, ending a point of contention and confusion. Part of the confusion originates from the fact that $\mathrm{d}$-functions are essential in the basis sets used to describe these compounds (or else unreasonably high energies and distorted geometries result). Also, the contribution of the $\mathrm{d}$-function to the molecular wavefunction is large. These facts were incorrectly interpreted to mean that $\mathrm{d}$-orbitals must be involved in bonding (Ref.1 and Ref.2).
For transition metal centers, the $\mathrm{d}$ and $\mathrm{p}$ orbitals are the primary valence orbitals, which are only weakly supplemented by the $\mathrm{p}$ orbitals (Ref.3). The question of whether the $\mathrm{p}$ orbitals actually participate in bonding has not been definitively resolved, but all studies indicate they play a minor role.

Indeed, the abstract of Ref.2 states that:

No evidence is found to support the traditional notions of $\mathrm{sp^md^n}$ hybridization.

But this article is not publicly available and it may not reflect the current scientific consensus. Making a long story short: Are the authors of Ref.2 and Steven Fawl correct? If so, is the bonding of every hypervalent molecule analogous to $\ce{XeOF4}$ (removing 1, 2 or 3 electrons from the valence shell of the central atom and $\mathrm{sp^n}$ hybridize it)?

References:

Eric Magnusson, &quot;Hypercoordinate molecules of second-row elements: $\mathrm{d}$ functions or $\mathrm{d}$ orbitals?,&quot; J. Am. Chem. Soc. 1990, 112(22), 7940–7951 (https://doi.org/10.1021/ja00178a014).
David L. Cooper, Terry P. Cunningham, Joseph Gerratt, Peter B. Karadakov, Mario Raimondi, &quot;Chemical Bonding to Hypercoordinate Second-Row Atoms: $\mathrm{d}$ Orbital Participation versus Democracy,&quot; J. Am. Chem. Soc. 1994, 116(10), 4414–4426 (https://doi.org/10.1021/ja00089a033).
Gernot Frenking, Sason Shaik (Eds), eds. &quot;Chapter 7: Chemical bonding in Transition Metal Compounds,&quot; In The Chemical Bond: Chemical Bonding Across the Periodic Table; Wiley-VCH: Weinheim, Germany, 2014, pp. 175-218 (ISBN 978-3-527-33315-8).
First, hybridization is a model used in Bond Valence Theory to explain the bond nature between some atoms in some molecules. Actually, the current binding theory is the Molecular Orbital Theory, in which we no longer use hybridisation. But, we study hybridisation because it is a simple and useful tool to explain a lot of compounds.

But, what the professor said in your question, it is not that the sp3d2 hybridization does not exist and cannot be used to explain any molecule. What he is saying is: In hypervalent compounds, there is evidence that the d functions do not participate in the bond.
After reading your question, I have searched a lot about the binding in hypervalent compounds. And what I found was that the nature of bond in hypervalent compounds like XeOF4 has been the subject of a lot of controversy for a long time, because in the represetative atoms, the energy gap between the nsp and nd orbitals is too large, so the d orbitals cannot hold extra electrons. And, nowadays we have evidence through ab initio calculations that the d-functions do not participate in bonding in hypervalent molecules. 

However, this is a recent evidence, so, if you have to awnser in a test about the hypervalent molecules, use the d-orbitals to explain them!

I am leaving some links with some articles and books that I read about this subject:

Chemistry of Hypervalent Compounds

The three-center-four-electron (3c-4e) bond nature revisited. An atoms-in-molecules theory (AIM) and ELF study

New bonding concept for Hypervalent molecules, including electron poor and electron odd compounds