On the other hand, natural selection runs on death and reproduction.

Humanity's genetics will naturally deteriorate without death.

Tech that gives you immortality probably gives you the ability to tune your genes and their expression too. We are, in fact, slightly closer to the latter than the former. Things like CRISPR, though yet fairly crude, are in practical use.

And humans haven't been subject to natural selection for ages. Pretty much the entire civilization is a cushion between you and forces of nature. Even mastering fire and learning to shoot an arrow from a bow were major developments away from natural selection.