I seriously don't understand why some people think Sage Mode is exclusive to Senju. Just because they have strong bodies? Minato, Jiraiya and Kabuto are nowhere near related to Senju, as far as we know. I think if they would be related to Senju somehow, the manga would have stated it. Still, you need a strong enough body and large enough chakra reserves to learn Sage Mode. Uchihas in general have large chakra reserves. We don't know if they have strong enough bodies, but if Minato and Jiraiya could learn it, I'm sure Uchihas could too. Kabuto is unique, as his body is manipulated beyond recognition.
No one has shown the feat of learning Sage Mode without help. And we have seen that toads and snakes have different Sage Modes. It is natural to THEM, and that's why humans need their help to reach Sage Mode. Do you think Hashirama or Naruto would have learned Sage Mode if they never met the toads? Without the toads' help, they would never learn Sage Mode. What if, for example, Sasuke or Madara (or any Uchiha) went to Ryuuchi Cave and the snakes would help them achieve Sage Mode? Presuming they meet all requirements, I see no reason why they couldn't achieve it. The fact that the manga has never shown an Uchiha with Sage Mode doesn't mean they couldn't achieve it. By this logic, only those shown in the manga could learn it. The only character other than SM users who wanted to achieve SM is Orochimaru.
The thing is that you have to meet all the requirements to achieve SM. Being Senju is not a requirement, however, strong body and large chakra reserves are. You also have to find the secret places.