Trying to stop natural selection would also involve halting any form of medical care and research worldwide — which would bring about an enormous and unnecessary death toll. Mankind would also have to cease all research in agriculture (and subsequent selective crop breeding), a shining example being the Green Revolution during the middle of last century which has been widely credited for preventing up to one billion deaths from poor food security worldwide.
Any arguments for the benefits of stopping natural selection by halting the progress of science and technology in this area just don’t align to a healthy and thriving society, anywhere — whether at the dawn of agriculture around 10,000 years ago (arguably one of the most important steps our species has ever taken)-or today.
We would also be losing a huge number of species which are currently protected by international law (tigers, pandas and many, many others) as well as the thousands protected and cared for by the dedicated conservation and zoological professionals and organisations worldwide.
Regarding non-native species, there is a comprehensive summary on Wikipedia here: https://en.wikipedia.org/wiki/Introduced_species
The section under terminology may be of interest to you in particular and does a great job of explaining the variations of this term and how they apply, much better than we could!