Old dutch families were definitely part of the highest social circles. However, they did not keep to themselves, but married into more numerous English, Irish groups as the years passed.

One can look at the Roosevelt family as a good example. Cornelius Roosevelt (100% dutch) was born in 1794 and was one of the richest New York merchants of his day. He founded the forerunner of Chase Bank, and was grandfather of Teddy Roosevelt. He was dutch, but married Margaret Barnhill who was of English/ Welsh/ Irish descent.
The Schuyler family was another Dutch family that maintained prominence long after New York left Dutch control. Alexander Hamilton's wife was a Schuyler. And then there were the Rensselaer family. Stephen Van Rensselaer (b 1764) founded the Rensselaer Polytechnic Institute, was a congressman, and prominent merchant. His mother was a member of the Livingstons another prominent (primarily Scottish) New York family. And he married another Schuyler... Finally, the Beekmans. A Beekman served as a governor of the dutch colony, and the family maintained its prominence in New York for many years.

In St Louis, Washington University was founded in the 1850s (at least partially) because the WASP middle/upper classes didn't want to send their kids to Saint Louis University, which was founded by French Catholics. They wanted a school that was "really American."

Great Heart of the Republic, by Adam Arenson, says that the university was founded as non-sectarian, but in reality it mostly attracted people uncomfortable sending their kids to a Catholic, and thus "unamerican," institution. He also writes that this was an era of nativist rhetoric, the rise of the Know-Nothing Party, and that calling new organizations "non-sectarian" was often an excuse for opposing traditionally Catholic organizations.

There was certainly somewhat of a preference or perhaps nostalgic reverence for those of Anglo-Saxon stock, but any professed Protestant was generally welcome in the United States. In the early years of the country, the Founding Fathers generally sought to promote immigration from Northern Europe -- the Huguenots were an exception -- although European immigration was rather slight in between 1776 and 1830 and most of these immigrants continued to stream in from the British Empire. By the mid-19th century, there was considerable alarm at the great number of Catholics entering the United States leading to a very strong nativist reaction against immigration.

Of course, there could be upper class Catholics. Charles Carroll was a signer of the Declaration of Independence, but Maryland was also a heavily Catholic state and he remained the only Catholic signer. The acquisition of Louisiana in 1802 likewise brought more upper class Catholics into the American elite although the French and Spanish gentry preferred to live amongst each other in New Orleans, thereby spurring the new American arrivals to build the "American Quarter" that eventually became the Garden District. Since a Pennsylvania Dutchman could be as American as a Connecticut Yankee, religious identification therefore became synonymous with a virtual ethnic group. Anti-Catholic sentiment often bound Protestants of utterly different denominations together and this would yield to outright nativism by 1850.

Interestingly, there were also several few upper class Jewish families living in the Deep South. Charleston was a prominent center for the American Jewry and they rapidly integrated into Protestant American society while retaining their Jewish identity.