Appointing a non-Catholic doesn’t “sidestep the problem” if the proposed ambassador is openly pro-death. For instance, the US ambassador to Israel is often non-Jewish, but Israel would likely not receive an ambassador who was an open Holocaust denier.
It might be easier to find a Protestant, Jew, or even agnostic or atheist who is silent on the issue, than a “Catholic” in good graces with the Democrat machine with such a zipped lip.