Hi, so I've been in the position your boyfriend is in. Strict parents, no dating approval, joined credit card (at the time), parents very involved in day-to-day life. When I was seeing someone in University, I hid it from them for the first few months because I knew my parents would not approve/lose their shit. I'd lie to them about where I was going, staying, etc.
However, parents can be strict as hell, but he is 20. And while yes, he's still in college, parents are paying for everything, etc. He needs to man up. It's clearly something that weighs heavily on your mind, and this kind of thing is not minor. You two are in a relationship, you're not just fooling around I'm assuming so you obviously care for each other, but he needs to stand up a bit. I understand that can be scary with strict parents and the culture, but it's either that, or he hides you? You'll begin to resent him, it'll effect your relationship, and if there's supposed to be a future, well, there is no way you should be the one footing the bill because his parents track your boyfriends every move.
I hate to say the word ultimatum, but I guess it's what it will come down to because it is what it is - he needs to either tell his parents and they'll have to deal with it, or you need to end things if he won't. It's not fair to you in any way. His parents obviously care about him. They'll deal with it, if it's such an issue at all.
I told my parents, and I was worried, and yes, my parents were initially mad. But you know what happened? They saw that I was happy, and my mom eventually said that as long as I'm happy, that she's happy. I was around your boyfriends age too, and I put my foot down because I cared for (my ex now) a lot. I didn't want to keep sneaking around, because even though she at the time didn't tell me how she felt, I could tell it was something that weighed on her mind. Talk to him, tell him everything you feel and see how he responds. If he's not willing to, I think you'll need to end things.