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I think natural evolution is accepted specifically because it's natural and therefore hard to stop. We would have to eradicate humans in order for our natural evolution to stop.
I also think genetic engineering and any "evolution" that may come from that is more frowned upon because it's unnatural and can lead to the feared "designer babies" as well as other issues.
Natural evolution is probably more accepted by the general population because it's the natural reaction of a species to stimuli from its environment. As opposed to genetic engineering which is an artificial and purposeful redirection of the course of human evolution. I know that there are many aspects of genetic engineering that's widely acceptable like eradicating chronic diseases from humans. But the possibilities of genetic engineering in the future such as superior humans would be detrimental to the rest of us. Whereas if superior humans came about because of natural evolution, that'd be more acceptable because it was natural and it would just be our species reacting to our environments.