What we know for sure is that Luffy's bodily fluids obviously aren't rubber. He bleeds, salivates, sweats and pees. However, I always thought he was literally rubber for the most part. Quite obviously his muscles, veins, nerves and bones are, if not rubber, similar to rubber, just like the outside of his body. Still, many other Paramecia fruit users seem to will themselves to change, and when they do, they're the real thing, they do not just resemble it. Like Mr. 1, for example.
Although Luffy seems to be rubber man 24/7, there are instances when he doesn't stretch, although one supposes he could, like when he's being held back by a crewmate. And yet his Devil's Fruit ability works automatically, even when he isn't expecting anything (Like Buggy's, but unlike Miss Valentine's). Is it possible that while some DF users will their abilities on, others will them off? If so, why would Luffy ever will it when in such situation that he needs to be held back? And if he can't will his ability off, why doesn't he wobble as he goes (rubber bones can't be all that firm)?
There are so many questions about it that Oda alone could answer, assuming that he has given it that much thought. This is starting to give me a headache and I haven't reached any kind of conclusion. Maybe we're thinking too much?