When militant atheists claim that they are oppressed by “religious privilege”, what they’re really doing is taking Christian privilege and misrepresenting it as “religious privilege” in order to erase the oppression faced by minority religions. Why? Because militant atheism requires that all religions be portrayed as institutions of systemic oppression.
In reality, it’s only Christianity which is privileged in Western culture. Judaism is totally appropriated by the “Judeo-Christian” colonial narrative, Islam is demonized to the point where numerous public figures openly declare that freedom of religion shouldn’t apply to Muslims, and all other religions are alternately denigrated and exoticized. Hell, even Christian privilege really only applies to sufficiently mainstream denominations of Christianity; non-mainstream Christian denominations are routinely vilified as “cults” just as non-Christian religions are.
In short, there is no “religious privilege” because there is no form of systemic oppression which is unique to atheists and does not affect other minority belief systems. Atheists are subject to a degree of oppression in Western culture, but it is due to being non-Christian, not due to being specifically atheist .