As I understand it, a neutral mutation is simply a mutation that does not change the protein produced at that locus, therefore doesn't change the phenotype.
Your understanding is incorrect. A neutral mutation is neutral with respect to fitness. It may change the phenotype, but not every change in the phenotype has a positive or negative effect on fitness or is subject to selection.
And a changed phenotype would have to spread through the population to have a part in forming a new species or breed etc. That spreading would be the result of some form of selection, something that favors that phenotype.
The genes for the change in phenotype can spread through drift and they may never reach a large proportion of the population. Almost all populations consist of individuals that are not identical genetically or phenotypically. The individuals that make up the population have many thousands of traits that each vary with gaussian-type distributions.
As I keep pointing out, if you keep getting mutations eventually you lose your species or breed.
In this case breeds and species are not similar because breeding has a goal of creating purebreds.
Nature has no goal of "pure species", and as is observed, species vary greatly in thousands of traits and mutations keep adding variety in every
surviving individual in every generation.
I note
surviving individuals because obviously
lethal mutations are eliminated. Often detrimental mutations are not passed on or are passed on to fewer offspring.
Highly beneficial mutations may eventually reach fixation in a population, but most mutations, even beneficial ones are at lower proportions in the population.
Some breeds have to be artificially preserved by enforced reproductive isolation but it is that isolation that keeps such identifiable populations identifiable and intact, protecting them from the gene flow that would destroy their recognizability.
And again, this may apply to selective breeding, but there is no biological boundary protecting natural populations from the gene flow that would destroy their recognizability.
Billions of years of fossil evidence and observations of the living species in the present demonstrate that despite millions of species going extinct, millions of species survive and continue to evolve on the Earth today.
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