The article uses the world "evolution" but there is no evolution here.
The common term is "transhuman" but there is no reason to think anyone will stop being human.
The Church cares about your soul and there is no reason to think people are not going to have souls.
The writer seems to be looking for a fight for some reason.
Some of the proponents of transhumanism are vehemently anti-Christian and try to paint an image of Christianity as being completely against scientific advancement.
As some have already pointed out, there are many instances of transhumanism that the church actively supports. Prosthetic limbs, glasses, modern healthcare, etc.
Where the battle occurs and should occur is with respect to the sanctity of human life. Most Christians don't oppose stem cell research, but they do oppose creating human embryos only to kill them in research.
Genetic engineering is an area where we need to tread carefully. I suspect most Christians would fully support genetic modification treatments to overcome genetic diseases.
But if you start doing things like mixing human and animal DNA, is that not bestiality?
If we get to the point where we understand genetics that we can safely modify the creator's design, should we? There is no scriptural prohibition that I see. How do you get to a safe understanding without having horror stories and mistakes along the way?