Is it possible we've been misinterpreting the emphasis of this passage all along? As in, when we read it, we assume it's emphasizing the animals that are allowed, and by implication stating that all other animals are disallowed. Grammatically, it is at least equally possible that it is the "may" that is to be emphasized, implying that this is a change to a previous rule in which the students were not permitted to bring those animals.
For example, standing school policy for years prior to Book 1 could have been that students were not allowed to bring owls, cats, and toads. If that was a well-known rule in wizarding circles, then the school would make sure to let all students know that the rule had changed as of this year. The letter should then be taken to mean "(This year, a change to the rules has been implemented. From now on,) students may bring an owl or a cat or a toad." All other animals not listed have always been allowed (including Percy's rat and Lee's spider), and now this year, three animals that had previously been banned are now acceptable as well.
There is no canon to back this up, to my knowledge*. I merely point out a grammatically acceptable interpretation of the letter's passage.
* We know that Percy had owned Hermes since he became Prefect in his 5th year, but that was also Harry's first year, which is when the new rule would have come into effect. I do not know of any other examples of students bringing owls, toads, or cats to Hogwarts prior to the start of the books.