but there is RPL1 up to RPL41, and same for RPS and then MRPL and MRPS , so despite the similarities, one can argue different organisms may have different rRNA genes.
RPL1 and such are genes for ribosomal proteins. I'm talking about the genes that encode the ribosomal RNA subunits. These genes are used to infer the evolutionary relationships of the tree of life, so presumably they are shared across all known organisms, or else it would not be possible to infer a phylogenetic tree.