Pretty much the same question than Are the Donald Duck comics on-topic?, although different characters, as so far, it doesn't seem we discussed either Bugs Bunny or the Looney Tunes on Meta. We have three looney-tunes questions but two are about Marvin (deffo on-topic), another is Bugs Bunny picture book involving a machine that creates carrots, which motivated this Meta post.
That said, we would consider talking animals to be part of a fantasy if:
They had been uplifted in some way (either by technology or magic)
Their speaking was somehow fantastical to the other characters.
I am no expert on Bugs Bunny, but I don't think he fits either of those? As for "tackling the SFF elements in those", we have three Bugs Bunny questions:
- Novel about Bugs Bunny being tricked by a wealthy man to loot some snowy building which already spawned some heat in the comments. One side argues anvils fall from the skies, the other argues that the anvils are just generic kids cartoon weirdness, not really on-topic.
- Bugs Bunny picture book involving a machine that creates carrots same arguments could probably go on for a new round.
- 1990s cartoon movie - Bugs Bunny anti-drugs video is unavailable but this looks just like an anti-drug PSA? Is that really on-topic?
- what to do with those? Leave them all open? Close some?
- in the future, are all Bugs Bunny stories on-topic the way Donald Duck was?