"Are you a dog person or a cat person?"

Both--

"Waffles or pancakes?"

Neither- I used to like both, but I came to the realization that I don't like sweet foods for breakfast

"Is it pronounced *this* or *that*?"

I really hate when people argue over the pronunciation of things- As long as people know what you're talking about, it doesn't matter how it's pronounced -.-

"Are you a morning person or a night person?"

I'm a sleep person 💀