Was Albus Dumbledore disrespectful towards Petunia Dursley by informing her about her sister's death in a letter, not personally, and basically forcing her to give Harry Potter a houseroom?
Yes, Dumbledore should have spoken to Petunia in person instead of just leaving Harry on the doorstep with a letter, but I would use the term “wildly inappropriate”—”respect” has nothing at all to do with it.
Also, Dumbledore did not force Petunia to take Harry in. Petunia had written a letter to Dumbledore as a child, [DH ch 33] and she could have just as easily written a letter to Dumbledore again, telling him to take Harry back.
So, Petunia obviously took Harry in because she cared deeply about her sister, right?
Petunia and Vernon took Harry in with the explicit intention of abusing him. If anyone lacked respect, it was Petunia. She had no respect, compassion, or empathy for her dead sister or for Harry.
PS ch 4: "We swore when we took him in we'd put a stop to that rubbish," said Uncle Vernon, "swore we'd stamp it out of him! Wizard indeed!"
There is Uncle Vernon explaining exactly why they took him. They wanted someone to abuse—Vernon, because he was a Sadist who hated magic and James Potter, and was eager to take it out on his kid (remind you of someone? 😛) , and Petunia, who hated her sister because she was jealous that Lily was a witch, and was eager to take out that jealousy on Harry.
Here is the rest of the scene which makes it all perfectly clear:
"You knew ?" said Harry. "You knew I'm a—a wizard?" "Knew!" shrieked Aunt Petunia suddenly. "Knew! Of course we knew! How could you not be, my dratted sister being what she was? Oh, she got a letter just like that and disappeared off to that—that school—and came home every vacation with her pockets full of frog spawn, turning teacups into rats. I was the only one who saw her for what she was—a freak! But for my mother and father, oh no, it was Lily this and Lily that, they were proud of having a witch in the family!" She stopped to draw a deep breath and then went ranting on. It seemed she had been wanting to say all this for years. "Then she met that Potter at school and they left and got married and had you, and of course I knew you'd be just the same, just as strange, just as—as—abnormal—and then, if you please, she went and got herself blown up and we got landed with you!" Harry had gone very white. As soon as he found his voice he said, "Blown up? You told me they died in a car crash!” […] "Load of old tosh," said Uncle Vernon. Harry jumped; he had almost forgotten that the Dursleys were there. Uncle Vernon certainly seemed to have got back his courage. He was glaring at Hagrid and his fists were clenched. "Now, you listen here, boy," he snarled, "I accept there's something strange about you, probably nothing a good beating wouldn't have cured—and as for all this about your parents, well, they were weirdos, no denying it, and the world's better off without them in my opinion—asked for all they got, getting mixed up with these wizarding types—just what I expected, always knew they'd come to a sticky end—"
Petunia was happily married to a man who thought that her sister deserved to be murdered. They abused Harry mercilessly.
So who is the really disrespectful person in this equation?
As to Dumbledore, his problem wasn’t lack of respect.
It was a lack of good judgment.
Dumbledore was a neglectful ass for leaving Harry at the Dursleys without ever once personally checking in on Harry to make sure that they weren’t abusing him.
People always assume that Dumbledore knew how badly the Dursleys treated Harry, because he knew that Harry would face ”ten dark and difficult years” [OotP ch 37] but he didn’t specifically know how badly they were abusing Harry (but he should have—so it doesn’t really make his neglect any better).
Mrs Figg was a Squib. She did not have X-ray vision—she couldn’t see what was going on inside the Dursley house, and she only had Harry over at her house a couple of times per year at most.