@froovyjosie So, at this point you are in a space where you want to explore Judaism more. You also seem to want your parents to know and to approve. Along the lines of what @lucillelucillelucille said, beliefs are very personal, and so in the end this is your decision and your life.
Regading what @marinelife said, I prefer to be open with the people closest to me, to share my life. I prefer to give them the chance to be accepting. I feel like this has risen to the level of a secret right now in your mind, and secrets can be a big burden. I am going to compare it to a child who thinks they are gay. I know many people who waited to tell their parents they were gay much longer than necessary. So worried about what their parents would think. Their lives and feelings had to be a secret, even in the one place that should make us feel the most secure, our homes with our parents, who love us more than children can ever know. Eventually the truth is usually told or comes out, and usually the parents accept it, many say they always knew and its fine, although there are some parents that do reject the idea and it causes a bad rift. Usually there is no bad rift though or complete rejection. But, I find these adults tend to be more to themselves about private matters, don’t reach out to family for help and support when in need, and carry that into their SO relationships. I know I am going to get slammed by people on this thread for saying all that, and of course this is not true for everyone, but that has been my observation.
It is not a judgment, I am not saying people who are more private and to themselves are wrong or bad, but I like being able to be completely honest with the people closest to me, especially when living with them. I feel it builds better bonds and closer relationships. You seem to be the same. And, I should say that sometimes it really is better not to tell parents who will be awful, but I assume if you are considering telling them they are not going to do anything extreme. Most atheists I know don’t dislike theists, they dislike people who want to convert everyone, and who let what they feel is magical thinking interfere with life and learning, or who are hateful and judgmental. Reformed Judaism does none of these negative things.
Sometimes people say things behind closed doors, because there is no one around it might offend, but it does not necessarily mean they judge or are hateful. I hear people all the time say things that would be perceived as racist, but I know them well enough, and their actions, to know they aren’t. So, your fear of telling them might be worse than the reality.
You are still exploring, just tell your parents that, read some books. Buy the Idiots Guide to Jewish History and Culture. It is funny and informative about the culture of American Jews. A temple where I lived in FL gave an introduction to Judaism class for Jews and gentiles, not a class to convert people, and it was very good for the basics. Maybe a temple near you has something similar, or a college level course in a local college. There is no rush, take your time. Religion and beliefs is a process over a lifetime usually.
Were your parents raised atheists when they were children?