"Old Mr. Bunny had no opinion whatever of cats." What does it mean?

Looking in Google books, many of the instances of "had no opinion whatever of" X mean that he literally didn't have any opinion of X. However, there are a few instances of this phrase meaning "did not think highly of X"¹. For instance, Google books gives (Blackwood's Edinburgh magazine, 1885)

Flies! The landlord had no opinion whatever of those puny hooks with little tufts of feather upon them, which Mr Howard called flies. He would like to show them something that was a fly indeed: a marvel of mechanism, wound up by clock-work and kept thus in motion for twenty minutes at a time. That was a fly, ...

It's clear from the context that the phrase "had no opinion whatever of" means "did not think highly of" here, and given the context, I believe its use in Benjamin Bunny means the same thing.

¹ I would have used "thought very little of", but in the context of the original phrase, it's too ambiguous.

The explicit meaning of the sentence is that Old Mr. Bunny did not have an opinion either good or bad or complex or nuanced about cats, that he just didn't think of cats at all. The intended meaning is that he wasn't scared of cats, differently than one might expect of any rabbit.

If you don't think much of something, you have a low opinion of it. Here the phrase is intensified: Old Mr Bunny had such a low opinion of cats that he didn't hesitate to attack one.

In British English, they use whatever where an American would be more apt to use whatsoever, with an extra so packed in there. It means he had no opinion about them at all.