Something with DNA, the Rinnegan's Genetic Code is still in there, for both the Senju and Uchiha. It all depends if its dominant and recessive genes. The sharingan was a mutation. I still believe Naruto can some how awaken it, if he's pushed enough. When the Senju and Uchiha DNA combine, the Rinnegan became a dominant gene again and awaken. Naruto still has a chance to awaken it on his own, or with a help from a Uchiha. I feel like Naruto best chance to awaken it is, through getting all the chakra from Kurama. Since the tailed beast, have effects on the person they are sealed in, Look at Naruto whiskers, that suggest that Kurama's chakra influenced part of Naruto's DNA, who know's what happens if he gets all of Kurama's Chakra, it would be flowing more, and might cause some effects to Naruto.
Well, from what Itachi said and seemingly Sasuke confirmed, the tablet (seen with a normal Sharingan) says that anyone that achieves MS, obtains power to control the Kyubi (this might have been actually added by Madara or some other Uchiha that had seen him control it with MS, since one needs only a Sharingan to see it - it's actually easy to differentiate what Sage wrote and what someone else did, since the text written by Sage speaks of possibilities in a more philosophical manner, while the ones not by him are more like instruction about gaining power).
Originally Posted by paulbee
Also, it's important to note that while Madara might have used his MS/EMS to gain control of Kyubi, Obito didn't, rather he didn't have to. At that time, he already possessed the power of Hashirama Senju's Cells (which partially allows control of GM and the Jyubi which are the same more or less :P) and combined even with a basic Sharingan, it was enough to control the beast.
Seeing as even partial powers of Sage (Spiritual, Physical, or both) can give certain control over the Bijuu, GM-Jyubi-Shinju, it's possible that those partial powers actually resonate with So6p's power still mingled in the Bijuu (like for example the So6p's Sealing jutsu that Naruto was able to activate after gaining Kyubi's power, was this something within the seal, or something that came from claiming Kyubi's power, thus hidden within Kyubi ?). Of course, saying Shinju's power might be more accurate (since So6p's power is actually the fruit's), thus by using the Shinju's power, one can gain control over the Shinju's body and it's manifestations.
I'm not sure why but Madara's awakening of Rinnegan still seems a bit fishy, it's strange that his body would have been mutating for so long and awakened only right before his death. It almost feels like someone came, when Madara was the weakest (at his death bed) and aided him in awakening the Rinnegan without Madara even noticing.