As for the Bajorans I'm not sure they'd be unhappy to see Sisko leave at the beginning. They didn't like the idea the Emissary would be a non-Bajoran except for Kai Opaka. Later in "In The Hands Of The Prophets" he seemed to be pretty unpopular with the Bajorans. The Vedek assembly wouldn't see him, Bareil didn't want to be seen in public with him. They wouldn't even let their daughters date his son (poor Jake!). It took time for them to finally accept him.
I think the fact that Sisko got on well with Opaka at the start certainly helped. It's doubtful that what happened later would have happened if Opaka had still being there.
If anything Sisko being able to deal with the Bajoran political and religious sections probably helped him more than anything really. He could deal with the Bajorans.