Do you have a mechanism to explain HOW an animal can adapt in “the same way to the same environment”? Would it be natural selection of genetic variation? Divine intervention? A lamarkian will to change? What?
How does an animal adapt to its environment?
And if you accept that old world and new world vultures adapted the same way to the same environment (losing neck feathers to better feast on carrion) - then obviously a non vulture bird population “adapted” into being a vulture population in response to the “environment” of being a carrion eater - two different times in two different locations (the old world and the new world) from two very different bird lineages.
And a non vulture bird need not give birth to a vulture bird in one generation, as one unlearned entirely in biology would conceive of it - no more than a speaker of Latin would give rise, in one generation, to an Italian speaker unable to converse with his or her parents.
You say this is obvious, but it is not. In fact there is no proof that this ever happened. In fact you simply assume it happened. You don't think you have to prove it, because it's just so obvious. That's not science.
Natural selection is not the same thing as evolution. Natural selection is animals adapting to their environment. The theory of evolution goes much further and says that all animals are descended from one common ancestor. If you don't know the difference between natural selection and speciation, then you are in fact completely unlearned in the the field of biology, unlike me.
If the non-vulture became a vulture over many generations, (something you have no proof of) then it would at some point have stopped being a non-vulture, and become a vulture. All you have to do is prove that a non-vulture gave birth to a vulture at some time, but you won't ever be able to do that, because non-vultures don't give birth to vultures, they only give birth to non-vultures.