You are:
Pac-Man
Although I've never been interviewed,
How can you interview a video game character?
I'm famous all over the world.
Everyone's heard of Pac-Man.
People love to watch me eat,
People love to play Pac-Man and watch him eat, since eating increases their score.
But some disapprove of my habits.
It's not healthy to be constantly eating. Also, as JLee said, the ghosts don't like it when Pac-Man eats power pellets, because then they can be eaten.
I don't mind working for my food,
You have to run around all over the maze to eat all the dots, and when you want to eat ghosts they are always running away from you.
And I like to eat on the run.
Pac-Man almost always has to be moving in order to eat.
Picky, I eat only 3 foods,
Power pellets, dots, and ghosts.
Not counting my desserts.
The desserts are the Cherry, Strawberry, Orange, Apple, Melon, Galaxian, Bell, and Key.
I have very strange diet goals:
Eat 244 to 260 bites per meal,
There are 240 dots per board, 4 power pellets, and the ghosts can be eaten from 0 to 16 times.
Plus 2 bites of dessert per meal-
1 bite of one and 1 bite of another.
A fruit/key/galaxian/bell appears twice per board.
Timing my bites is important,
You don't want to eat a power pellet when the ghosts are far away, since you only have a limited amount of time to eat ghosts. If you chase a ghost too closely and it turns back to its normal color and then you touch it, you will die.
And when done wisely,
I can reach my full 260 bites,
And then I will be very happy.
You will get the max score per board if you eat all the ghosts while they are blue (and all the fruit/key/galaxian/bell). You will also be very happy if you do this on the first board because you will surpass 10,000 points and you will get an extra life.