The only lower ranks who would resent him being made captain after doing so are not worth a spit. It's they whom the service does not need.
Oh? And why is that?
If you've worked all your life to earn something -
anything - and then some pissant upstart is *handed* that thing on a silver platter, you are going to be resentful (and entitled to it), believe you me.
For example: At your place of work, wherever that may be, I'm guessing you've worked hard to get where you are. So what if some newbie walks in the door, fresh from his job interview, and is immediately made CEO? You wouldn't like that, would you?
If there's anybody on the
Enterprise who isn't a cadet

, and any of them decide to transfer off the ship because they can't stomach the idea of serving under some pipsqueak who didn't earn his rank (and please, don't tell me about saving the planet, even that's not enough*), I would sympathize with that. I might do it myself if I were in their shoes.
Now, if they remain on the ship, of course they should obey Kirk's orders as they would a real captain, but anyone who objects to the situation has every right to ask for a transfer.
*Look at
Nemesis, for example. Picard saved Earth in that film (it was clear that Shinzon would have destroyed Earth if he could have gotten near it), yet Starfleet didn't make him Admiral of the Fleet, did they? Of course in *that* case, they could have, since Picard was already a Captain anyway.