Mufasa does respect Zazu and Zazu respects him back that's why Zazu went along with it. He knew that it wouldn't get out of hand and he wouldn't get hurt. If he wanted he could have flown off at any time and that's it no more Zazu.
It's like in real life for me, I respect and love my friends to death but doesn't mean I don't start a play fight every once in a while ^^