My headcanon is, that after the nuking of Washington, the shell-shoked survivors of the US-goverment official capitulated, but this capitulation wasn´t accepted by great parts of the country and the army. But people like Hoover and Smith stayed loyal to the "legal" goverment and fought side by side with the Nazis against "muniteers" and "rebels". This "police action" lasted till 1947, but it created a special bound between the Americans and the Germans. Therefore the american Nazis honestly celebrate VD America and the Germans have give them a status as allies.
I like this explanation. It fits with what we see in season 1, where the Americans who serve the régime clearly regard themselves as being among the winners, instead of being a colony.
I can see Americans who side with the Germans but are not committed to Nazi ideology per se rationalising their collaboration with arguments such as 'the war is lost, the rebels are just anarchists making things worse', 'the old system has failed. It lost us the war. We need a national revolution. The Germans do have some ideas worth applying,' and 'by proving ourselves to the Germans, we can retain influence in our country and prevent worse from happening'.
Of course, such arguments seem pretty hollow when they're participating in mass killings and helping the Nazis carry out their extermination of 'undesirables', but this is the kind of mantra people would tell themselves to justify their actions. Of course, some would just sign up because they're ambitious and see an opportunity.