Sounds to me that you BOTH are old enough to make your own decisions for yourselves?
Granted, maintaining respect for all concerned is noble and admirable, but seems to me, in your situation, is it reasonable?

Two years into your relationship and his parents aren't even aware of you?
Ummmm.....WHY do you tolerate that? Can he not make decisions for himself? Is he so under his parent's control that he is forced to "hide' you from them?
From your description of him, it sounds as though he's still in High School....."Allowed to?"

No. You are not rude for wanting inclusion in his activities, especially considering that the activities you are requesting inclusion don't involve his parents, (from whom he is so inclined to hide you). Which makes me wonder....WHY not include you? Are you sure his parents are the ONLY reason for not including you?

This doesn't make sense to me, other than he is possibly hiding more from you than you care to want to face, or that he apparently is perfectly okay with keeping you at a far distance and has little to no intentions of including you in HIS (other) personal life. So long as you're fine with it and allow it to continue, why would he even think about changing it?
Seems he has best of both worlds...simply because you give it to him?

I hope the best for the both of you.

Shangrala