The comment from @PlutoThePlanet, "The right to not get sport-murdered", whether meant as a joke or as an answer, is the extent to which we know about Dumbledore's support for Muggle rights. We know that Dumbledore's support for Muggle rights doesn't include the right to be left alone to mind their own affairs.
In a letter to Grindelwald, Dumbledore writes:
Your point about Wizard dominance being FOR THE MUGGLE'S OWN GOOD -- this, I think, is the crucial point. Yes, we have been given power and yes, that power gives us the right to rule, but it also gives us responsibilities over the ruled. We must stress this point, it will be the foundation stone upon which we build. Where we are opposed, as we surely will be, this must be the basis of all our counterarguments. We seize control FOR THE GREATER GOOD. And from this it follows that where we meet resistance, we must use only the force that is necessary and no more.
So his attitude is "power gives us the right to rule", of might makes right. As the Muggles have no (magical) might or power, they have no rights, except that the Wizards are limited in using their power to what they think is good for those ruled, not that they would bother to actually ask what they want.
It should be noted that the very definition of the word "Muggle" implies they are too stupid to think for themselves:
I was looking for a word that suggested both foolishness and loveability. The word 'mug' came to mind, for somebody gullible, and then I softened it. I think 'muggle' sounds quite cuddly. (interview)
We don't know much about Dumbledore's interaction with Muggles, but what we know doesn't show him in a good light.
When he visited Tom Riddle in the orphanage, he used magic against Mrs Cole:
There was no doubt that Mrs Cole was an inconveniently sharp woman. Apparently Dumbledore thought so too, for Harry now saw him slip his wand out of the pocket of his velvet suit, at the same time picking up a piece of perfectly blank paper from Mrs Cole’s desktop.
'Here,' said Dumbledore, waving his wand once as he passed her the piece of paper, 'I think this will make everything clear.'
Mrs Cole's eyes slid out of focus and back again as she gazed intently at the blank paper for a moment.
'That seems perfectly in order,' she said placidly, handing it back. (HBP)
As the muggle ministry is aware of magic, it should be no problem to have some official documentation to give her to keep. Instead she is missing one of the children she is responsible for, and in case there is an audit, all she can say is that she thought everything was fine, but she doesn't have any proof to present, so she would be in serious trouble.
Later, he drops Harry at the Dursleys' door without bothering to ask their opinion. He doesn't even have the decency to tell Petunia in person that her sister is dead and that she is supposed to raise Harry.
Dumbledore stepped over the low garden wall and walked to the front door. He laid Harry gently on the doorstep, took a letter out of his cloak, tucked it inside Harry’s blankets and then came back to the other two. (PS)
In fact, in OotP he admits that he knew how Harry's childhood would be, so he was fully aware that the Dursleys don't want Harry.
You had suffered. I knew you would when I left you on your aunt and uncle’s doorstep. I knew I was condemning you to ten dark and difficult years. (OotP)
In book 6 when he comes to retrieve Harry, he conjures three glasses of mead and levitates them, banging against the Dursleys' heads, validating their fears that magic might be used against them. This is not just disrespectful, it is plain rude, and I don't think he will find a convincing argument that it is for their own good, or even for the greater good, it is just petty and shows that he is a bully who likes to annoy people who can't defend themselves.
So there is no evidence that Dumbledore promoted any Muggle rights, and if he did, it was likely for political maneuvering and not because he believed them to be what is right. His personal opinion about Muggles is the same as the author's, that they are fools and need to be told what to do, and can be used for entertainment.
The difference between him and the Death Eaters is just in the details. Dumbledore thinks it's fine to have some fun with the Muggles as long as they stay alive, while the Death Eaters don't have that restriction.