As soon as I got to the part where you wrote "...and he's 27", I almost laughed out loud. He is much too old for you to "get him" to break up with anyone. Your right to decide things like whom your children date ends when they are an adult. It's great that you care about your children, but there will naturally be limits on how much you can control them as they get older.
Here's another thing to think about. Just because someone you love doesn't want you to do something, that doesn't mean you are going to agree with them. For example, if your son wanted you to stop going to church, would you agree and stop going? No, because going to church is important to you, and you like it, and so you're going to keep doing it. And if afterward, he kept on pestering you to stop going to church, would you start to think he was right? Not very likely; if anything, you'd be angry/upset at him for FAILING to see that going to church is meaningful for you. Realize that he may be feeling this same way towards your attempts to make him break up with this woman.
Also, pay close attention to this part that you wrote: "last night he got really angry and told me that he doesn't want to hear about it any more or I won't see him again if I try to bring that up one more time"--this type of statement is a lot more serious coming from someone in their late twenties than it would be if your son was a teen. I would advise you to think hard about whether your disagreement with him over dating this woman is so important to you that you are willing to lose your relationship with him completely over it. If so...that's your choice, but I thought I should mention it.
Another thing that you said that stood out to me was: "she's Atheist and that goes against our family values and morals". What do you mean by "our" values? "Our" as in you+your husband+your daughters? Or are you including your son in the collective "our"? The reason I am pointing this out is that children can develop a different set of morals than that of their parents, and so it may not be correct to say that his dating this woman "goes against our family values" if you are including him in that collective "our", because from his own perspective dating her may fit perfectly in with HIS own values.
You also wrote, "I don't understand what's wrong with him there are so many beautiful and sweet girls at church and he had to choose someone like her. I can't believe it". Please remember that there is more to loving someone than just finding them attractive and nice. For example, these church women that you say are attractive and nice may not get his jokes, not have the same ideas about raising children, not share his passion for such-and-such hobby, not want to live in the same state he wants to, not have the same taste as him in literature and movies, etc, etc. I have met many men that were good-looking and nice that I would not date--is there something "wrong" with them or "wrong" with me? No, their personalities were simply not a good fit with mine. It would be unfair to them for me to start a relationship with them if we did not really click. (Also, just because you find the women in your church pretty doesn't mean that your son does...)
At the end of your question, you put "he had to choose someone like her. I can't believe it". Here's something that might help you believe it a bit more: Sometimes, in their enthusiasm to promote their religion, parents get on their children's nerves. So, rather than think "My goodness, I don't know why he wants an atheist girl in spite of the family he was raised in being super religious!" you might want to consider the thought that maybe he wants an atheist woman BECAUSE the family he was raised in was super religious.
Here's another quote from your question: "I'm really concerned that she influences my son and he starts having all those crazy ideas that she has." Has it ever occurred to you that your son's girlfriend may feel the same way about YOU? From an atheist point of view, believing in a god is a crazy idea, but do you want her to respect your belief in your god? Sure you do, and I'm sure she would likewise appreciate you respecting her LACK of belief in a god.
...Also, she might not actually be "influencing" him at all with her views--do you even know for sure that he wasn't already atheist (or agnostic) before he met her? Because you didn't mention HIS stance on religion in your question.