These are called highly conserved sequences [1] meaning that they reappear all over the evolutionary tree and studying how they mutate is how we got a lot of our most fundamental knowledge about evolution, especially the first few billion years.
The peptidyl transferase center that helps form the main catalytic binding site [2] on ribosomes is so conserved that it’s immediate ancestors could predate protein synthesis altogether (it’s made of RNA instead of amino acids). Some like the Hilstone H4 protein mutate so slowly that there’s a two amino acid difference out of 102 across complex multicellular organisms, so it’s thought to be critical for gene expression. Then there are ultraconserved non-coding elements which haven’t changed all even though they seem to be unexpressed introns.
There’s lots more like that, many of them used to align sequences so we can actually compare genetics across species.
[1] https://en.wikipedia.org/wiki/Conserved_sequence
[2] This is what uses the 3’UTR to know when to terminate the protein sequence.