Gay or Straight? Should they tie the knot?
Seeing as how the creators of Bert and Ernie have time and time again asserted that Bert and Ernie are in fact not homosexual, this is a non-issue.
I think its pretty reasonable to assume that the creators of a story or character have the final say in these matters, as it is their sole right to determine basic facts about the story/characters which they have created.
Saying B&E are gay, in the face of the creators, who maintain that they aren't, is like saying the character of Jim in Huckleberry Finn isn't black. The creator has deemed what their characters are and aren't, let's leave it at that, because, really, we don't have any say in the matter.
Long story short, no. They should not get married.