I'm not a cunning linguist, nor a middle eastern expert -- but my Dad is Iranian and Muslim, as is 1/2 my family, and being "not from here" means I've been more observant of different cultures than most.
When you say "Fuck you" to someone, it rarely means want to copulate with them. And when middle easterners say some phrases like Death to America", it probably shouldn't be literally translated either. While other phrases like "Allahu Ahbar", should probably be parsed quite carefully, and noted in context. Those that don't, are probably trying to propagandize you on something, like the NYT or CNN does.
Death to America
Ayatollah Khomeini and the Islamic Republic of Iran, popularized the term, "Marg bar Āmrikā" or "Death to America", and it has become part of that culture, but is also used by many Arab countries as well. And for some, quite predictable reasons, Americans can be a bit disturbed by calls for their violent elimination.
When asked what it means, their government officials stated, "we mean death to American politics, not the American people. We do not really want death to anyone. The slogan is simply against the interference of those governments [i.e. US, and Israel]". Uh huh. A bit overstated, but the point is that the term is more nuanced that many realize.
There are certainly a few in Iran that are fanatics and would kill us all, if they could. Just like a few in America might do the same back. So I'm not saying there's isn't a threat in the phrase: there is. But when you see big protests of people chanting it, they know what they mean, and for most, it is not that they want to kill all Americans. They also say, "death to..." France, UK, Soviet Union, Israel, and have said "death to (their own President)" when they were pissed at him, and lots of other things/places they didn't want to kill. It’s not usually a literal translation, any more than when Americans say "Fuck France" they're not calling for the gang rape of everyone in France.
There are dozens of American idioms that other cultures don’t understand: "I don’t care", "I hate you mommy", "Bless his heart", "Let’s have lunch”, “shooting the breeze", "do I look fat in the jeans".... if you literally translate those, you're probably missing the point. You have to understand a culture and it's history, and judge it by what they mean, not what they say. Especially a culture as rife with Tarof (ritual politeness or impoliteness) as Iran (or Japan). They both say things politely that they don't mean, and say things in anger that they don't mean. So they're being culturally insensitive by not getting how others take it, but we're being as culturally insensitive if we don't try to understand across the cultural barrier as well.
Middle easterners are tribalistic, arrogant, prone to exaggeration, conspiracy theories, perpetual victimhood, cultural narcissism, and they have a slightly different value of life. But most of them go to protests because they're bored, want to be part of something bigger, and just want to party in a country where kicking a ball in a dusty mine field is entertainment. So try not to read more into it than is meant.
The context for the phrases origins was the West in most of the middle east, had fucked with them and played with their countries/governments like pawns. The U.S. was far less bad than the U.K., France, Russia or some others, but in Iran at the time, the U.S. had been the most recent manipulator of their country. So "death to America" (shorthand for American Interventionism in the middle east) became the rallying cry of the revolution. Just like in Vietnam, many were willing to rally around Ho Chi Minh and the Viet Cong, because they wanted autonomy... only to find out later, that their own leaders were bigger assholes than their foreign puppets were. But they still wanted to be free to tyrannize, bully, and fuck up their own country.
However, there's a balance. When people intentionally mis-translated as, "Down with America" instead of "Death to America", that's not good either. It does translate to "Death to America", it just USUALLY only means "Down with America" in common usage. But it's still a bit dishonest to mis-translate it that way, or ignore that there are a few where it's quite literal. When Iranian people are complaining about American support of Israel, or intervention, it's probably not literal. When their leadership is trying to rile up the masses in a government sponsored protest, it might be. Context matters.
Ironically, the same outlets like the NYT or CNN that want to do gymnastics to understand the metaphor and soften it, when it comes to Iran, will intentionally do the opposite whenever it's someone with an (R) after their name speaking (especially Trump). Any slip, exaggeration or idiom becomes an opportunity to play gotcha, and show those outlets bias/hypocrisy/double-standards. So I often whine about that double standard, or sort of over-simplifications. But in the case of "Death to America" they're actually more right than wrong.
Allahu Akbar is not a benign phrase that "God is good", as many try to mislead others, it translates to "My God is greater" (than all of your God(s)). And they mean it quite literally like that.
Some Fake News outlets like the NYT will try to sell you on some fictionalized version of their truth -- that it's just a casual every day phrase like saying "how's the weather", or "we should do lunch", but that's propaganda, and another example where their readers get actively dumber by believing what they read in the Times.  Yes, it can be used like that. Just like some friends might use, "yo mama was a ho!" as a light hearted greeting. But that's not really what it means in most common usage, and context means a lot more than the phrase (which dishonest outlets will ignore). When someone is murdering someone else while saying it, or using it in the context of Jihad, it's more than just a casual turn of phrase. Just like "Black Lives Matter" might mean something benign, but in the context of the BLM movement, it means what the sum of their actions are: it means that you need to buy into the lie that cops target innocent blacks, and that you hate the cops/authority, and so on. NYT either knows that and are being dishonest, or they're too stupid to pay attention to.
The middle east, and middle easter Islam, is not a humble culture -- it is arrogant, tribalistic, victimized, narcissistic and intolerant. Allah is the name of THEIR God. We can debate whether they truly believe that their God is the same God as Christianity or Judaism, with a lot of varying opinions -- but the simplest way to think of it is that they are ethnocentric (like most cultures), and the personification of their God is NOT the same as the personification of the Jewish or Christian God, even if it's supposed to be the same being.
Which is why the interpretations of how each behaved, or would react to an event, is so different. Allah is much more Arab-centric, far less loving/tolerant/forgirveful, far more vengeful and tolerant of bloodshed and punishment towards those violating the tenets -- so when a Muslim is referencing Allah, they're not usually talking about Jesus's sacrifice, the trinity, or turn the other cheek. It's ethnocentric of westerners to assume they mean it that way. They most often mean it as in "our God is pissed that you treated us (the only people that matter), wrongly", or "our God will smite you, or tolerates us smiting you in his name". Don't let any news outlet bullshit you on what the underlying intent is, in context. Most people might not even mean the underlying intent in casual usage -- but there's a reason it evolved to be in casual usage, and that is definitely, "we think our God/Culture/Beliefs are better than your God/Culture/Beliefs".