You actually have it backward. The KMT were the Nationalist under Chiang Kai-shek. Mao's forces were the Red Army (shortened from "Chinese Workers' and Peasants' Red Army", although I cant find the acronym for them).
You... MIGHT have seen instances where the Germans sided with Mao to fight the Japanese
As far as I am aware, the Germans never gave aid to the Red Army (that was almost all the Soviets doing). In fact, many of the Nazi party members who were pushing for a Chinese alliance did so on the grounds of helping the Nationalist to defeat the Red Army. To that end, they did give a surprising amount of aid to the Nationalist in the form of officer training, rifles, machine guns, and even a reasonable amount of anti-tank guns. But only ever enough to show the Chinese they were serious, since they were afraid giving too much would turn the Japanese against them.
China and American might have been allied during WW1 and best buds at the time, but by WW2 China had basically undergone... uh... SEVERAL political revolutions, so the ruling political faction really had no correlation between then and now.
The bigger problem between the US and China was more the lack of a strong central government to do anything meaningful with. Kai-shek (the "official" leader of China at the time) was generally on fairly good terms with the US, and even if he had some issues with Gen. Stilwell was still appreciative of American supplies and backup (especially in the form of the Flying Tigers when that was finally set up). However, the central government under Kai-shek controlled very little in the way of true territory, and between them the rest of the country was under the control of various warlords because, truly, there is nothing new under the sun. And many of those warlords ranged from lukewarm to America to outright hostile. IIRC, that incident you cited of the American and Chinese troops "joking" about shooting each other was actually troops from one of the warlords rather than KMT troops.
Then there's the added fun that the entire conflict between China and Japan started in, what, 1938? 1939? When was that stupid conflict on the bridge - bah, whatever. Too tired to do the research.
1937, with the Marco Polo Bridge Incident.
Conversely, America would get stuck in a two-way war between Germany/China and Japan... then again, would America even be fighting Germany by this point?
It does actually cause quite the butterfly effect. Germany thought it was inevitable they would have to fight the US because of Lend Lease aid to Britain, but at the same time Hitler was always hesitant and didnt actually declare war until the Japanese attacked Pearl Harbor, and he only did that because it was obliged by treaty. So there is a solid case to be made the little cold war between the Germans and the US would continue until Hitler thought it better.
I am also skeptical about how much a Chinese/German alliance would really do to the US. Most of the Chinese leadership that mattered for overseas relations were friendly with both the Germans and the US, so they would likely try to find a way to square that circle and just not get involved. On top of that, China lacked any real ability to project power, as their navy was virtually nonexistent as was their air force. But you may see a shadow war start up in China between German and American advisors similar to any number of US vs. Soviet proxy wars in the Cold War, and perhaps even go so far as trying to fight over those warlords I mentioned previously. This does probably mean that the Red Army gets a pretty significant setback though, as they will lose out on Soviet supplies when the Germans invade and this time they are unlikely to get American supplies like they did IRL.
If I am honest though, it is probably the Japanese who get hosed in this situation. They are not going to avoid war with the US (since they considered it their destiny to fight the US), BUT their industry was only at the point it was even in 1941 because they had a lot of German advisors improve their industrial capabilities in preparation for war. In this alternate timeline, that probably doesnt happen, and Japanese industry remains notoriously inefficient to an even greater degree than we know IRL. It would still be a hard war, but there would probably be less aircraft and some ships would take longer to complete (if they complete at all), so it could change the outcome of the war and cause the collapse of Japanese forces faster than the 6 months proposed by Yamamoto (a prediction he was right almost to the dot about, by the by).
It is honestly probably one of the more interesting alternative histories that doesnt get as much looks at it because not a lot of people in the West know about the war between Japan and China (kind of like how the Pacific front itself is surprisingly sparse in pop media).
Just to help with some of it:
You actually have it backward. The KMT were the Nationalist under Chiang Kai-shek. Mao's forces were the Red Army (shortened from "Chinese Workers' and Peasants' Red Army", although I cant find the acronym for them).
As far as I am aware, the Germans never gave aid to the Red Army (that was almost all the Soviets doing). In fact, many of the Nazi party members who were pushing for a Chinese alliance did so on the grounds of helping the Nationalist to defeat the Red Army. To that end, they did give a surprising amount of aid to the Nationalist in the form of officer training, rifles, machine guns, and even a reasonable amount of anti-tank guns. But only ever enough to show the Chinese they were serious, since they were afraid giving too much would turn the Japanese against them.
The bigger problem between the US and China was more the lack of a strong central government to do anything meaningful with. Kai-shek (the "official" leader of China at the time) was generally on fairly good terms with the US, and even if he had some issues with Gen. Stilwell was still appreciative of American supplies and backup (especially in the form of the Flying Tigers when that was finally set up). However, the central government under Kai-shek controlled very little in the way of true territory, and between them the rest of the country was under the control of various warlords because, truly, there is nothing new under the sun. And many of those warlords ranged from lukewarm to America to outright hostile. IIRC, that incident you cited of the American and Chinese troops "joking" about shooting each other was actually troops from one of the warlords rather than KMT troops.
1937, with the Marco Polo Bridge Incident.
It does actually cause quite the butterfly effect. Germany thought it was inevitable they would have to fight the US because of Lend Lease aid to Britain, but at the same time Hitler was always hesitant and didnt actually declare war until the Japanese attacked Pearl Harbor, and he only did that because it was obliged by treaty. So there is a solid case to be made the little cold war between the Germans and the US would continue until Hitler thought it better.
I am also skeptical about how much a Chinese/German alliance would really do to the US. Most of the Chinese leadership that mattered for overseas relations were friendly with both the Germans and the US, so they would likely try to find a way to square that circle and just not get involved. On top of that, China lacked any real ability to project power, as their navy was virtually nonexistent as was their air force. But you may see a shadow war start up in China between German and American advisors similar to any number of US vs. Soviet proxy wars in the Cold War, and perhaps even go so far as trying to fight over those warlords I mentioned previously. This does probably mean that the Red Army gets a pretty significant setback though, as they will lose out on Soviet supplies when the Germans invade and this time they are unlikely to get American supplies like they did IRL.
If I am honest though, it is probably the Japanese who get hosed in this situation. They are not going to avoid war with the US (since they considered it their destiny to fight the US), BUT their industry was only at the point it was even in 1941 because they had a lot of German advisors improve their industrial capabilities in preparation for war. In this alternate timeline, that probably doesnt happen, and Japanese industry remains notoriously inefficient to an even greater degree than we know IRL. It would still be a hard war, but there would probably be less aircraft and some ships would take longer to complete (if they complete at all), so it could change the outcome of the war and cause the collapse of Japanese forces faster than the 6 months proposed by Yamamoto (a prediction he was right almost to the dot about, by the by).
It is honestly probably one of the more interesting alternative histories that doesnt get as much looks at it because not a lot of people in the West know about the war between Japan and China (kind of like how the Pacific front itself is surprisingly sparse in pop media).