This is such a landmine topic, because most countries did this, including the UK and the US; see e.g. the MS St. Louis. This is why there are several "heroes of the resistance" that in modern parlance are "people smugglers", forging credentials and visas in order to help people escape.
Today you see exactly the same hostile attitudes to non-white refugees of basically every war except Ukraine.
Many people in the British Empire were told to fight for the mother country or even to preserve the empire (which was largely gone by the seventies, with some major territories becoming independent in the later 1940s.)
“Go save the Jews” was hardly a motivating factor for any nation in the war.
Difficult to pin something as all consuming as WW2 on "about" anything, but we can look at who fired the first shots, which was clearly the Japanese invasion of Manchuria in the east and the German invasion of Poland in the West (followed shortly after by the USSR invading Poland and later Finland from the other direction.)
It is not at all a given that, had Germany stayed within her international borders, that the Holocaust would have on its own triggered WW2. After all, mass murder in the Congo Free State didn't trigger invasion of Belgium.
IDK if things have changed but generally the whole narrative in the US is presented as unwitting yankies discovering the horrors of the death camps. It's debated how much some levels of the government knew, but it certainly wasn't public knowledge in the US.
Well, that or fighting the Japanese.
Patriotism and threat seem to have been the main motivators for most people in the west.
Interesting connection, as her father was a foreign member of the Nazi party (while living in Brazil) and had lied about his Nazi affiliation in the past. When he moved back to Germany, he joined the main party.
Perhaps that's because most of those refugees could more easily shelter in neighboring countries that they are more culturally similar to... if shelter was actually the primary thing that they were seeking.
That is 1930s pre-war Germany and Austria; and around 550k people by the most generous calculation. Yes, the world wronged them. But you cannot say death camps happened because the US didn’t hand out enough visas.
After 1939, when Germany invaded Poland (home of 3-3.5m Jews) and in 1941 the USSR (home of another 1-2m Jews) no one was being forced to leave (or live) anymore. People were being killed with bullets to the head or back, and when this started to be unbecoming/too inefficient, the German state devised an industrial approach to the killing of humans.