As for why this affects gram negative bacteria more strongly, I can't
say because I'm not familiar enough with the relevant microbiology.
Perhaps gram negative bacteria are more sensitive to certain
incorrectly-synthesized proteins. Another possibility could be that a
mutation that compensates for streptomycin could result in
hyperaccurate phenotypes that make gram-negative bacteria less
competitive/more vulnerable? I'm just speculating at this point. I'm
sure that some microbiologists could offer a better explanation.