Humans have many variants
There is variation. The project I use to help understand this natural variation is gnomAD.
Using VarMap and a slightly out of date gnomAD file, I counted
16007805 protein-coding variants across the human genome. This number will only go up over time.
Indeed, the 1000 Genome project found that on average each person has between 250-300 loss of function protein variants that are not found in their parents (The 1000 Genomes Project Consortium, 2010).
This is an important concept for human health.
ClinVar is one of many projects that aims to catalogue and study when these variations lead to disease in a clinical context.
Another is the 100,000 genome project by Genomics England which studies NHS patient data in cases of rare disease and cancer.
Haemoglobin has variants, including disease variants
At the time of writing, HBA1 (haemoglobin alpha subunit gene) has 183 gnomAD variants and 17 pathogenic variants in ClinVar (sourced from gnomAD).
Again, both of these numbers are likely to increase because the data will cover more people.
Constraints on highly important proteins
But the underlying question is, I think, "are there some proteins that are so important, that life keeps them highly constrained" i.e any variation will lead to an invalid cell or a disease phenotype.
gnomAD attempts to add "constrained" metrics to each protein record, and some are more constrained than others.
Haemoglobin scores a pLI of 0.01 (higher scores are more intolerant to variation, specifically loss of function variation).
p53 is a gatekeeper of the cell cycle, mutants of which are common in cancer cells. It has a pLI score of 0.53 which means it is very intolerant to variation compared to haemoglobin.
Ribosomal protein L5 has a pLI of 0.998 implying it can tolerate little if any variation.
The ribosome is critical in protein production, hence altering it may cause a complete breakdown of cellular life.
Variation and Evolution
There is an almost philosophical difference between human variation and human evolution. Variation is a static snapshot of our protein sequence from individual to individual. Evolution in the sense of a Dayhoff Matrix requires looking back millions or billions of years by comparing similar protein sequences across many species.