With sh.
#!/bin/sh
SBI=abc,def,ijk
MEM=one,two,three
out=$(
  while [ -n "$SBI" ] && [ -n "$MEM" ]; do
    sbi_first="${SBI%%,*}"
    sbi_rest="${SBI#*"$sbi_first"}"
    mem_first="${MEM%%,*}"
    mem_rest="${MEM#*"$mem_first"}"
    SBI="${sbi_rest#,}"
    MEM="${mem_rest#,}"
    printf '%s_%s,' "$sbi_first" "$mem_first"
  done
)
echo "${out%,}"
With bash
#!/usr/bin/env bash
SBI=abc,def,ijk
MEM=one,two,three
while IFS= read -ru3 str0; do
  IFS= read -r str1
  out+="${str0}_$str1,"
done 3<<< "${SBI//,/$'\n'}" <<<"${MEM//,/$'\n'}"
echo "${out%,}"