No, this is not true, and this is because you do not understand.
Yes, it appears to protect you from some variants, but not from others. If you are exposed to a variant, like the Delta variant, that it does not protect you from it does not give you any protection.
By vaccinating everyone they create an environment where all the variants that you are not protected from will become prevalent. If you only vaccinated those who were most at risk, perhaps 5%, then those variants would not become prevalent and the vaccine would be far more effective for those who need it most, ie it would save more lives.
As for "do you believe in evolution" I have no interest in that debate. I qualified the remark saying "survival of the fittest". That is a very biblical concept. This is why Paul says physical exercise has some benefit. What Darwin actually observed was "survival of the fittest". He theorized a process which has since been debunked mathematically as being an impossible explanation.
Now some will say that since I am protected from some variants that is better than nothing. Again, that is not true. They have forced your body to make antibodies specific to one feature of one virus (spike protein) and therefore you have fewer non specific antibodies. That makes your immune response to all other viruses weaker. This is not simply a theory but has been shown with peer reviewed studies. A good analogy is the Magino line, a very robust defense of the French border with Germany. It would have worked great except that Germany drove through Belgium and around that wall. If France had had tanks instead of a wall (non specific antibodies versus specific antibodies) they would not have fallen to Germany in two weeks.