I don't know, I do not think nature is of a very stable nature
It is impossible to try to stop evolution...It is part of nature.
The question is how you select animals for breeding... Most ppl do not have the heart to breed for viability, nature is cruel. Some breed for colour or pattern. Most breed everything, thinking no change has taken place... I.e. we breed the genes that would be eliminated by selection pressure, this will change colour, behaviour, morphology etc over time... All for the worse seen from their functionality in their natural niche. One cannot preserve a species without access to the selection mechanisms of their natural niche
Species do cross geographical borders and cross-breed. Species are just an old tired biological concept to try to differentiate animal genotypes and phenotypes on a timeline. It is an abstract division of animals to ease human understanding of evolution. Genotype and phenotype transitions are not abrupt but smooth with many animals caught between our simplifications. Think biological traits and normal distribution. Species is not absolute just a tool, an average with a standard deviation and confidence interval.
If two very different animals can breed, will breed and produce fitter offspring than two similar animals, then that offspring will prevail. This is nature. Is this not the process we should idealize..
Then again as Mark says, it all depends on why you want to breed animals. Many want a pet with a good temperament, interesting behaviour and nice colours for their enjoyment. That is fine. I am one of those people. But don't trick yourself into thinking that this corresponds with preserving a species