I never really thought of Charlotte's Web by E.B. White as fantasy (and definitely not science fiction), but it's definitely not realistic; now that I am thinking about it, I realize that it has many talking, intelligent animals, and is probably as close to fantasy as it is to any other genre. Also, I have a question I am dying to ask about it, and this site is the only one with a possibility of the question being on-topic.
The highest-voted answer to Are anthropomorphic animals by themselves enough to deem a work fantasy? tells us that:
Anthropomorphic/Sentient/Talking animals don't, in and of themselves, make a film/book/TV programme/comic into a fantasy if the central conceit is that talking animals do already exist within that fictional universe.
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.
Neither of these is the case in Charlotte's Web. All the animals are able to talk to each other as a matter of course, and there's nothing fantastical about this. None of the humans except Fern can understand them, but the in-universe explanation for this is that Fern is younger and more sympathetic and listens to them better. The only animal who shows abilities beyond that of a normal animal is Charlotte, and she's just unusually intelligent rather than being "uplifted" by some technology or magic (or being bitten by a radioactive human).