We found that 60 percent believed that atheists would not allow them First Amendment rights and liberties. More specifically, we asked whether they believed atheists would prevent them from being able to “hold rallies, teach, speak freely, and run for public office.” Similarly, 58 percent believed “Democrats in Congress” would not allow them to exercise these liberties if they were in power.Incidentally it is true that many Americans want to strip each other's rights; for example, a large group (the numbers are presented in a confusing way) would deny white supremacists the right "to give speeches in the community, teach in public schools, run for public office and other liberties."
This study's authors go on to say that while some atheists and progressives do want to deny political rights to Evangelicals, that number is smaller than the number of Evangelicals that want to deny rights to atheists. Evangelical fear of progressive power, they write,
comes from an inverted golden rule: Expect from others what you would do unto them. White evangelical Protestants express low levels of tolerance for atheists, which leads them to expect intolerance from atheists in return.I suspect that this is true, if you simply ask atheists about firm believers; the "leave them alone in their silly attachment to the Iron Age" attitude is common among the atheists and agnostics I know.
But I suspect that you might get a very different answer if you asked progressives instead about tolerance for people who think homosexuality is evil. I am quite certain that most progressives and atheists don't want people who believe homosexuals are all going to hell to teach school, and you can, in fact, get fired from teaching public school for saying this to you students. People who are tolerant of religion in a vague, general sense may nonetheless be very intolerant of many beliefs actually held by religious believers.