Well, Galatians513 wasn't entirely clear, simply referring to "contradictory" morphological and genetic "trees". I've clarified in the angle brackets above, but a couple things might be meant. For instance one might also refer to what might be called "typological" classifications of organisms. These would group organisms according to "type," without regard to evolutionary relationships. Contrasting would be "evolutionary" classifications, which group organisms according to the inferred typology of evolutionary relationships.
Conventional taxonomy tends to conform to patterns of evolutionary relationships, just because it was originally oriented (under the guidance of Linneaus in the 17th Century) to the pattern of "groups within groups" that is a relect of evolution. Of course a creationist might argue that God simply decided to create according to a pattern of groups within groups.
Therefore the most interesting cases are those were "typological" and "evolutionary" classifications do NOT agree. In these instances creationists would expect new lines of comparative data (discovered subsequent to the gross morphological criteria on which classifications were initially based) should conform with typological rather than evolutionary schemes. Evolutionists would expect the opposite.
A couple concrete instances come to mind. (I'm sure that many more would occur to a trained biologist.) For instance (as I mentioned in another context recently) even though crocodiles are classified as "reptiles" along with snakes and lizards, they actually share a more recent common ancestor with birds. This kind of situation can arise whenever a particular lineages "diverges" sufficiently in a particular direction -- as birds did in adapting to their peculiar form of locomotion -- that we decide it should have a new name.
Not surprisingly (to the evolutionists) the proteins and DNA of crocodiles are more similar to those of birds than they are to those of snakes or lizards.
Another example concerns humans. Genetically, chimpanzees are actually more similar to humans than they are to their fellow pongids (great apes) gorillas.
In these crucial cases, the evidence conforms with common ancestry rather than typology, contrary to what would be expected if God created "types within types" (by non-evolutionary means).
Rather, common ancestry is supported by morphological (typological) genetic, and temporal evidence.
It's actually well-known that there is considerable incongruence between various morphological trees and genetic trees. And genetic trees don't always resolve an ancestral relationship either because the different loci within the same species often show incongruence. 100% congruence is rarely found.
There are several reasons for this. Homoplasy and recombination make resolution sometimes very difficult. Plus, the correspondence between genotype and phenotype is rarely one to one. What's more, tree construction is based on data sets with varying ratios of signal to noise. One can imagine that morphological data sets are incomplete and very noisy, yet, the classic trees were constructed with them.
There are some examples where the genetic data has turned the morphological relationships completely on their heads.
Here are a just few references out of the many hits on a search for discordance/incongruence-morphological-genetic/phylogenetic incongruence, etc.
Syst Biol 1999 Dec;48(4):683-714
Data set incongruence and correlated character evolution: an example of functional convergence in the hind-limbs of stifftail diving ducks.
McCracken KG, Harshman J, McClellan DA, Afton AD.
Proc Natl Acad Sci U S A. 1994 Oct 11;91(21):9861-5.
Molecules vs. morphology in avian evolution: the case of the "pelecaniform" birds.
Hedges SB, Sibley CG.
To be sure, this doesn't turn common ancestry on its head, but it is important to remember that in biology, things are never very clean.