Over the past 25 years (if not more) it's pretty clear that nuclear weapons are seen as the biggest threat to the world (in regards to conflict) with outrage over Iran, North Korea and now Russia all testing and indicating they have nuclear weapons. So why doesn't the US see more backlash or anger over their use of nuclear weapons in the bombing of Japan?
I find it odd that it's not seen as literally one of the worst, if not the worst act of war and one of the worst things a country has ever done. Totally understand a lot of bad things were happening in WW2 but given how many innocent people were killed and continue to suffer to this day it's strange no one really views it this way.
This is a very loaded question, and not a very historical one, but I will just point out that there are plenty of people who think that the bombings of Hiroshima and Nagasaki were terrible and unjustified. It is frequently invoked in discussions that also include the Holocaust.
The reason that there are many people who support the bombings is that they believe (rightly or wrongly; the history is quite complicated) that they were successfully used to end further bloodshed. So the argument is that they were the lesser of two evils, and as such even though they involved a great loss of life (in a war that was itself full of great losses of life), they ultimately prevented a greater loss of life. You also have to keep in mind that (rightly or wrongly) a lot of the world was not especially sympathetic to the plight of the Japanese at that time, given the atrocities that the Japanese military had committed against its neighbors.
One can certainly disagree with that position along numerous lines of argument (historical, philosophical, ethical, etc.), but that's the argument that your post seemed unaware of. In the United States today, public opinion is pretty evenly split over whether the atomic bombings were justified/necessary or not.