If you are not a child of this person, then I don't see where you have any rights. You can contact the guardian but that person is in control. A Judge has ruled your family member needed a guardian and assigned one. To override this means lawyer and a lot of money.
When the county gained guardianship of my stepFIL it was because he wouldn't allow any of us close and local family members to help him (and we honestly didn't want guardianship or control, we just wanted to help him). Lutheran Social Services was his guardian and they were good at listening to our concerns, like when he was moved to a facility an hour away and it created a hardship for us to take his disabled wife to visit him. They moved him closer, but the cost was a lower quality Medicaid facility. The guardian allowed us to visit him, asked us what his likes and dislikes were, etc. BUT this is because we were close to him for decades. I don't think the guardian in your case is going to be as open, since "becoming more involved" is now too late. Why do you now want "rights"? You will have to go to court for this and it won't be worth it. Just be glad he is getting care, and it's not from you. Visit him -- that's the best thing you can do for him. If you think his care is lacking you can probably report it but it may not go anywhere.
You may be able to see him, but as for deciding his medical decisions and choosing a facility... that ship has sailed. If a court appointed guardianship, it was for a good reason.
Submit an application for contact to the guardian. You will have to explain where your uncle's loving and concerned relatives were while your uncle was becoming so incapacitated that the court agreed he needed a guardian's protection, but assuming you can give satisfactory explanations there is no reason why the guardian shouldn't agree that it is in the ward's best interests to maintain relationships with his family. It's only the ward's rights that matter, you see.
What are you looking for?