I believe that the consensus, for life on Earth at least, is that any kind of independent origins of life or proto-biotic systems must have fused symbiotically at some point, before the Last Universal Common Ancestor. Or at least the LUCA of "proper" living organisms, non-virus.
If different "lineages" with spontaneously formed RNA and whatever else, arose at some point, whatever happened after that, resulted in all living organisms having still the same universal genetic code, or just minor variants.
For total clarification, "genetic code" here isn't in the "genome" sense (which, albeit also is largely shared between lineages, isn't "universal"), but the relationship between codons, short DNA sequences that compose genes, and the amino acid synthesized from it. That's supposed to have been something that evolved, that could have been more different, not so much an inherent biochemical property.
I think it's possible that there could have been somewhat radically different basal biochemistries/phisiologies even from the same instance of origin of life. So, here on Earth, we could have two (or more) lineages that split very early on, and they could differ so much that it would even be debatable whether there was a common origin, or whether more instances of the same general process happened at isolated sites, with more than one of these original life forms surviving to this day. But, as it seems to be the case, even the most unrelated organisms aren't so different that they can be argued to have had a separate origin.