Family Guy is a comedy, and bestiality has been a comedy target basically since the dawn of man. As long as you're not portraying it as acceptable, political correctness will okay it (in the Family Guy universe, Brian's behavior is "acceptable", but there's also the grander implication that the universe itself is absurd/insane, and thus the implied synthesis is that it's only considered acceptable because the people are insane).
What you also need to understand is that "secular" people don't have a big problem with sleeping with an individual with animal anatomy (Brian is for all intents and purposes a human in a dog's body). Their big problem is sleeping with an individual with an animal mind. Popsci media has ingrained it into their coconut brains that animals are literally furbabies and thus it follows that only a pedo would engage with a furbaby. The fact that both of them end with "-philia" sadly drives this association even closer in the popular mind. This is of course trivial to disprove, but it requires active participation of the coconut brains and they're definitely not up to the task.