It is seriously hard to say whether Dumbledore is gay or not. I have read one of the books, but have also seen most of the movies (my mom is a fan) and not once has Dumbledore's sexuality been brought up at all. I have 3 theories on this subject:
1-J.K. Rowling was wanting a good buzz for the Harry Potter books and movies. She may have thought that maybe demand was going down and wanted to create some sort of extravagant detail that would shock people, but would also make everyone aware that her franchise was still up and running.
2-Rowling is English, and in England, being gay really isn't a big deal like it is in the United States. Maybe she was getting some flack from the gay community that there wasn't a gay character, so she just said that to appease the gay community.
3-Dumbledore is gay. She is the writer, so only she would really know (and Dumbeldore, if he were real). Who are we to really say anything otherwise?
As for Bert and Ernie, if they were really gay, wouldn't they be sharing a bed instead of sleeping on twins? Just a thought. I think it was more that they could only afford a 1 bedroom place, and it was a Felix and Oscar kind of situation (except for Ernie's weird obsession with his rubber ducky...I would think that more people would be concerned about his love of an inanimate object than him loving Bert).
And Tinky-Winky (the purple Telletuby) is gay. He has to be. He is purple. He carries a purse. He's a guy. And please, don't try to say that that big red purse is his 'man bag' or something like that. It was a purse. But I think that since it was a younger kids show, they can't go right out and say that yes, this Telletuby is gay since tolerance of gay people wasn't as good as it is today (even though that was only 10 years ago.
Timon and Pumba is a little bit harder to comprehend. In the movies, I know that they were always around each other, and didn't have any specific love interests. However, Pumba farts like there is no tomorrow. I know a lot of gay people, and trust me, they don't 'fart'. It is not their thing. Timon may have had some feelings for Pumba, but by watching the Lion King 1 ½ I figured out that Timon was Jewish (it is hard not to tell). I'm not saying that all Jewish people are straight, but usually Jewish families are close-knit, and they also have really close friends as well which would explain the closeness of Timon and Pumba. Nathan Lane is gay, and I know he was saying that he thinks Timon and Pumba are gay, but that is almost like saying that Eric McMormack (Will from Will and Grace) is really gay, or Will is really straight, neither of which is true.