1) Those people are bad because having gay sex is unnatural, a sin, and comparable to having sex with kids.
2) Those people are bad because they are denying others a basic human right.
You can obviously tell the difference between the two view points, right? One is hate speech and the other is not. But even still, under her comparison, the police chief could be fired if the right words were used. For instance, "people who only have sex with those of the opposite sex and forbid homosexuality are akin to bestiality and pedophilia"... yeah he could get fired for that.
That's a fireable offense anywhere. Here's a pro tip to managers: don't publicly write that a group of people who could work for you are as bad as horse ****ers and you probably won't get fired.