How do I stand up to my parents and maintain my relationship with them?

I have been with my boyfriend for 3 years. Our relationship is serious and we want to move in together. I am 22 years old and still depend on my parents for a lot of things, like my taxes and being on their phone plan and insurance and using their car. They are strict, conservative Catholics and don’t believe in sex before marriage and they are always talking about what a shame it is that my cousin lives with her boyfriend. I have never done anything to go against them in my life. I hide the fact that I am sexually active, agnostic, and many of my political beliefs from them for this reason. I am afraid of how they will react if I tell them we want to move in together and because I have never tested these boundaries I have no idea what their reaction will be. I’m not afraid of losing the material things (although it would be inconvenient) as much as I am of ruining our relationship, which is very good right now and very important to me.

How would you broach the subject? Am I being silly for being so nervous about this and if so how do I get over it?