Consider the following image which shows the resonance structures of $\ce{CO_3^{2-}}$ ion. What is the hybridization of $\ce{O}$? How do we proceed in such cases? In one resonance structure, the top oxygen has $\ce{sp^3}$ hybridization and in others, it has $\ce{sp^2}$ hybridization. In the hybrid structure, shown in the second image, I don't even know how to proceed.
The only important thing to consider for the description in terms of hybridisation is the molecular structure. It is therefore irrelevant if you are using a resonance structure, all resonance structures, or the resonance hybrid, or even some kind of completely different diagram. The structure for all of these is the same.
Therefore, to determine a reasonable hybridisation scheme, you should first look at local coordination of the atom. Please keep in mind that the $x$ in $\mathrm{sp}^x$ doesn't need to be an integer value.
For this, please look up Bent's rule and Coulson's theorem. You may start with my answer here: How is Bent's rule consistent with LCAO MO theory?
Please also keep then in mind that only orbitals hybridise and any combination of hybrid orbitals my be a valid description.*
If you keep this in mind, the following definition makes quite a bit more sense, hybridization in the Gold Book (DOI: 10.1351/goldbook.H02874)
Linear combination of atomic orbitals on an atom. Hybrid orbitals are often used in organic chemistry to describe the bonding molecules containing tetrahedral (sp³), trigonal (sp²) and digonal (sp) atoms.
Considering this, here are some zero order approximations, which my come in handy:
| Coordination | Examples | Approximate Hybrid Orbital |
|---|---|---|
| linear | carbon in acetylene or carbon dioxide, or any terminal atom** | sp |
| trigonal | carbon in $\ce{CO3^2-}$, boron in $\ce{BH3}$, carbon in acetone | sp² |
| tetrahedral | carbon in methane, sulfur in $\ce{SO4^2-}$ | sp³ |
| bent | oxygen in water | sp² - sp³ |
| trigonal pyramidal | nitrogen in ammonia | close to sp³ |
| trigonal bipyramidal | phosphorus in $\ce{PCl5}$ | model breaks down |
| octahedral | sulfur in $\ce{SF6}$ | model breaks down |
After writing all this, I've realised that I have commented on this before: What is the hybridization of the carbonyl oxygen in a carboxylic acid?
Footnotes:
* The terminology we use for hybridisation actually is just an abbreviation: $$\mathrm{sp}^x = \mathrm{s}^\frac{1}{x+1}\mathrm{p}^\frac{x}{x+1}$$ In theory $x$ can have any value; since it is just a unitary transformation, the representation does not change, hence \begin{align} 1\times\mathrm{s}, 3\times\mathrm{p} &\leadsto 4\times\mathrm{sp}^3 \\ &\leadsto 3\times\mathrm{sp}^2, 1\times\mathrm{p} \\ &\leadsto 2\times\mathrm{sp}, 2\times\mathrm{p} \\ &\leadsto 2\times\mathrm{sp}^3, 1\times\mathrm{sp}, 1\times\mathrm{p} \\ &\leadsto \text{etc. pp.}\\ &\leadsto 2\times\mathrm{sp}^4, 1\times\mathrm{p}, 1\times\mathrm{sp}^{(2/3)} \end{align}
There are virtually infinite possibilities of combination.
Or see more: Are the lone pairs in water equivalent?
** I have written about this a few times already. These should provide also data: