I'm not sure what religion this woman practices, nor am I certain about yours. What I want to suggest to you today is that the Bible doesn't endorse "religion" either. In fact, the Bible endorses "relationship."
I'm also not sure how you acquired your personal beliefs. It's definitely your choice. I am so sorry and sympathetic to you because the woman who calls you a devil worshipper is really approaching you in a negative way. You seem like a very intelligent and research-minded person, based on your open-mindedness. You might find a resource called "Why I Believe" really interesting. 60% of the information presented is based on secular research (research conducted by non-Christians who do not practice any religious beliefs). You can check it out online at www.lote.org and search for Why I Believe. If anything, this resource would give you in-depth information about the Bible, it's origin, it's accuracy, and why so many people put their faith in Jesus Christ. I hope you'll check it out sometime, when you want to truly understand why Christians believe what they believe.
As for me, I apologize for this woman's attitude. The Bible says in Romans 6:17 that all men (and women) are slaves to sin, and therefore, are owned by that sin. Sin, in the Bible, is personified. It's primarily used as a noun (only a handful of times it's actually used in verb form). So, from her perspective, she sees you as one who chooses to follow the devil. I know you don't believe in the Bible or the devil, but I would ask if you have actually read or studied it in any detail?
The Scripture that this woman is referring to is actually there. From a Biblical standpoint, we are part of two families (two lineages). One is Adam's (Adam and Eve) and the other is Jesus Christ. We are all born out of Adam's lineage. And, according to Scripture, we are slaves to sin, a.ka.: Satan. So, from that frame of mind, one is either reconciled to God through Jesus Christ and adopted into God's family, or one remains in Satan's family. There is no in-between according to Scripture. It's either from God, or from Satan.
I think she probably reacted harshly with her words out of her own fear for you. To Christians, we worry that others do not know the truth, and not knowing and accepting the truth is the absolute worst thing that can happen to someone. I'm not going to argue with you about your beliefs, or try to persuade you to believe mine! : ) What I would like you to do, is consider obtaining some really sound information, like the resource I suggested, that presents both sides (Christian vs. Non-Christian), and then conclude that you do not believe in the God of the Bible. I don't know if you have continuously encountered these personalities (like this woman who insulted you) throughout your life, and that has convinced you that the Bible and Jesus Christ/Christianity is not for you, if you did some research, or if you just came to that conclusion through other means and experiences. Just consider, with your common-sense and open mind, that what if you were actually wrong about the Bible, and God? You have to put the woman out of your mind and all bias and feelings aside, ask yourself that question. I had to ponder over that question, and I came to the personal realization that if I were wrong, if God DID exist, and if Jesus truly died for me, my eternity could be at stake.
I didn't believe in God either, until I truly began researching Scripture and it's origin, among other things. The "Why I Believe" series by Chip Ingram is the best information I have found, to date, that answered some of my questions in layman's terms. You can also go to a website called www.wayofthemaster.com and go through the Intro there. I'm sure you'll recognize a popular 80's actor who helped found the site. Anyway, he poses some really good questions that I think all of us should at the very least consider.
Many blessings, and again, I regret that this woman used those terms when she approached you. At the very least, had you been equipped with sound information about Scripture, you could have truly put a sock in her condemning mouth! : ) If she was out to witness to you, she didn't do a very stand-up job!! Rest assured, not all people of faith will react this way to your beliefs!