Given that quantum tunneling has been proven to be a cause of genetic mutations, I think it's certainly reasonable to claim that MWI is a good explanation of abiogenesis, if abiogenesis is determined to be extremely improbable.
The people claiming that "not everything happens with equal probability" really don't seem to know what they are talking about and should read about the problem with probability in MWI (spoiler: there is no such thing as probability in MWI), and explanations of apparent probability such as Deutsch's decision-theory approach.
Given that quantum tunneling has been proven to be a cause of genetic mutations, I think it's certainly reasonable to claim that MWI is a good explanation of abiogenesis, if abiogenesis is determined to be extremely improbable.
The people claiming that "not everything happens with equal probability" really don't seem to know what they are talking about and should read about the problem with probability in MWI (spoiler: there is no such thing as probability in MWI), and explanations of apparent probability such as Deutsch's decision-theory approach.