It's also medically incorrect. When you get a vaccine you are literally getting a live virus injected into you. There's no difference for your immune system. One isn't "fake" and the other "natural". Period.
To your point, viruses mutate and so similar to the flu and flu vaccine, if COVID-19 continues to mutate in ways that are different enough we'll have to get new COVID shots which use modeling to predict the likely virulent strains. People that are aghast about this concept are not really understanding the new reality we're in. The only hope is that if enough people get vaccinated quickly enough, a new strain won't mutate and cause the vaccines to lose some effectiveness. I think that's a wildly naive hope, though and the best path forward is just treating this like a worse flu and moving on with our lives.