If New Amsterdam survives until the Napoleonic Wars, and then is annexed by Britain, then what would its attitide to America be, and what would Americas be to it?
Lets assume a butterfly net allows New Netherlands to get most of NJ-Lowet NY-CN. The US is formed on schedule, and has Dutch lands spereating its north and south.
I think it is more plausible that the city and colonial councel of New Netherlands and New Amsterdam would chose to join the USA. As a percaution to be occupied by the UK. Since there were many internal troubles in the Dutch Republic from 1780 onwards, it is also likely that this happens even before the French Revolution.
The city and hamlets were ruled by a civil counsel and the director of the WIC, had to deal with them. Most likly the WIC was not in charge in the colony after 1665 and the city of New Amsterdam was granted city rights if it remained Dutch.
As mentioned in other posts, it was not a matter of nationality ( the concept did hardly excist at that time) but free dom and self determination. As in the Dutch Republic, this was found in New Amsterdam, the freedom of concesnes and the opportunity to make your fortune.
So it is not a matter of the number of Dutch colonist or English or German. The lingua franca was (form of) Dutch, as a language of trade and administration.