Atheists are the most distrusted of all of America’s minorities. When inquiries are made as to why this is so the response is usually that since God is the source of all morality, and since atheists do not believe in God, atheists have no morals.
Morals existed before religions. Morals governing behavior were absolutely essential in the social groups humans formed to enhance their survival in prehistoric times. Morals existed in civilizations before Biblical times in the form of laws governing commerce, criminal behavior, and disputes among the peoples. The Bible and Christianity are relative latecomers and plagiarized from the earlier sources.
Atheists, agnostics, humanists, and others give funds to charities like the Red Cross and the United Way. They volunteer in public service roles. Most of the time these works are carried out without identifying their non-belief, and why should they, as all humans should care about the condition of their fellow human.
The religious give to their church, and these funds are well defined. There is no mistaking the source of their generosity, especially when the bowl of soup comes with a sermon. The point being that the amount the religious give to charities is well accounted for, whereas the non-believer, giving to secular charities, is not so well differentiated.
In summary, the religious in this nation do not own morality. Their religious belief, their Bible, their god, is not the singular source of morality. Atheists, like theists, come from disparate origins and each has differing morals depending upon the particular societal group from which he/she came.
I suspect part of the reason for the mistrust is reason. Atheists, agnostics, and humanists deal in factual evidence. When the religious are exposed to factual evidence which contradicts their faith, there is a backlash. The truth, it seems, hurts.