This seems unlikely. It's usually considered that immunity to one variant gives you at least some immunity to other variants.
Could you provide sources for this claim?
If a new variant has a spike protein different enough, then you will not be in a better situation than an individual with no vaccine and no previous contact with the virus.
In contrast, someone with natural immunity would have the ability to produce a wider range of antibodies that target many different parts of the virus, therefore many more variants would be vulnerable to at least some of the antibodies.
(Caveat: the immune system actually is more complex than that)
That's quite a different claim to "it permanently reduces your body's ability to learn how to counter different parts of other versions of COVID".
> In contrast, someone with natural immunity would have the ability to produce a wider range of antibodies that target many different parts of the virus
This is a very different argument that natural infection gives more effective immunity than vaccination, and the empirical evidence does not seem to agree.
Here the argument is that, when the antibodies “learned” from the vaccine have a low, but not nil, effectiveness, then the immune system of a vaccinated person would continue producing only the same antibodies. A person with natural immunity would instead be able to modulate the immune response and use the most effective among the many antibodies that they can produce.
> This is a very different argument that natural infection gives more effective immunity than vaccination, and the empirical evidence does not seem to agree.
There is some evidence that natural immunity lasts longer, although it is not settled yet.