Wasn't Hyuuga once said to have been related to the Uchiha in some way, shape, or form? I believe that the blood connection could suffice if people are still upset about hyuuga not being good enough for Rinnegan. As for the Mokuton/Ice and such, only Hashirama had wood style yet there were many Senju. It doesn't take a certain elemental ninjutsu style to be able to have Senju blood. Yes, people are going to say "Oh, get an elemental KG before claiming Senju/Uzumaki/Senjumaki(I don't care)" Well, it doesn't just have to be mokuton. If the hyuuga were proven to be non-uchiha in any way, well screw it, we can say it is.
It wasn't an
official announcement that the Hyuugas are related to the Uchihas in some way, shape or form. It was merely an theory stated by Kakashi or some other person I can't remember. But yeah, I agree with you, Hashirama was the only Senju who possessed the Mokuton Kekkei Genkai as he was the sole user and creator of the advanced Kekkei Genkai before Madara implanted Hashirama's DNA into himself and Obito. You don't really need the Mokuton just to be a "legit" Rinnegan user. All you need to be is either an descendant of the Uchiha or Senju clan and transplant the other Rinnegan user's eyes into yourself like Madara did to Nagato. Hell, Nagato destroyed an
entire village just by using some borrowed power, yet, he possessed the Senju genetics whilst he doesn't possess the Mokuton. That was the reason why Nagato was able to use the said implanted eyes powers without requiring the Mokuton.
So my point is, no one needs to be a Mokuton user just to gain the Rinnegan, all they need is the genetics of both the Senju and Uchiha clan, however, they need a reasonable explaination how their characters are hailing from both Uchiha and Senju clan. However, I think it should take people some time/period before they can
really unlock the Rinnegan, you know, just like the Eternal Mangekyou Sharingan.
Even though I still dislike the Rinnegan by a very high degree.On the side note; If some people are
really that desperate for the Rinnegan then I would say they need to have a limit from using the Rinnegan. Nagato overused the Rinnegan for like 20 years or more prior the start of the Naruto series and he nearly died while confronting Naruto as the Six to Eight-Tailed Kyuubi. Obito can only use the Outer Path & the Human Path, but only to some extent. If he uses other paths then those two will it greatly consume his chakra. Madara could only use all the paths because he was born with an extremely high chakra stamina and by the fact that he's immortal, Nagato could only use all the paths as well because he's an Uzumaki, and as an Uzumaki, they are naturally born with a lot of chakra reserves and are blessed with an exceptionally long potential lifespan and strong life-force.