'to be' + past participle is a common construction for the passive voice, e.g.
I expected to be greeted on my arrival by someone.
We were to be disappointed by our accommodation.
The troops are to be deployed to forward positions.
We aren't the only ones to be completely appalled at the news of the cat suit ban.
is a perfectly acceptable and grammatical sentence.
The sentence that you provided:
We are not the only ones who feel completely appalled at the news of the cat suit ban.
is also a perfectly acceptable and grammatical sentence.
Both sentences convey exactly the same information. It would probably be possible to construct several other sentences that are perfectly acceptable and grammatical, and which convey exactly the same information. There is no reason to believe that any of those sentences are better than the others, or are to be preferred above the others.
The writer of the news article simply wrote a sentence that correctly presented the information they wanted to convey. Why did they use that sentence instead of the other sentences that they could potentially have used? Only the writer can answer that question.
There is not one exact rule for using the verb 'to be'. The verb 'to be' is one of the most widely used verbs in English (and most other languages), and takes many irregular forms. It would be impossible in a forum such as this to go through all of the rules, and the exceptions to those rules, that govern this verb.
I have attached a link, which may help you understand some of the complexity surrounding its use. I would recommend that you read a wide selection of grammar books, and talk to as wide a range of English speakers as possible, so that you become proficient in the many uses of this verb. The Verb To Be