No that's incorrect. If you don't hire someone because they're Muslim or Jewish or Christian or whatever, that's a crime.
Employment Discrimination Based on Religion, Ethnicity, or Country of Origin
Also, ones ideology could be considered their religion, hence making it illegal discrimination.
If an employer asks what your religion is at all that's officially illegal. Religion is legally speaking an off-topic zone for work in the US and if you as an employer or supervisor delve into religion with coworkers your organization/company can be sued for discrimination and pretty much in court the only question that the judge is going to care about is "Was religion brought up at all?" and if the answer is yes then that's the case, the accuser of religious discrimination wins because a company/organization cannot legally bring up religion as an issue with regard to work and there's no way to disprove said entity didn't use such info to discriminate somehow.
Now that said, do a lot of companies do it anyways assuming you won't spend the money to actually sue? Yeah. But I've seen companies pay big time for it when someone recorded the interview. Big payday in court.