Some said they felt embittered or hurt by criticism of the project, and of Islam in general, yet understood opponents’ misgivings. Others said Muslim-Americans should continue to push for the center’s construction as a means of asserting their full citizenship rights — but not too hard, lest they draw even more resentment. A few said they wished the project had never been proposed in the first place.

While these few dozen conversations do not represent the views of all Muslim New Yorkers, they show that many are grappling deeply, through the current tension, with the lingering ambiguities of their place in American society nine years after 9/11.

Malik Nadeem Abid, an insurance agent whose storefront window on Coney Island Avenue in Brooklyn framed a steady stream of men walking to pray at the mosque next door, said he was “not a big fan” of the decision by the Cordoba Initiative, a Muslim group that promotes interfaith cooperation, to build the center near ground zero.

“It was not a politically smart move, from my perspective,” said Mr. Abid, 45. “No one wants a center in downtown Manhattan that stands as a permanent fixture of this terrible tension.”