Depends on the doe. We have one that'll take any of the babies and isn't fussy. We have another, if her babies leave her for a day or two and come back (once they're of a certain age), she won't take them back, she's spiteful. "You don't want to stay with me? Fuck you then, go back next door".
She will foster young kits though (before they're old enough to start being adventurous).
The second doe we have is pretty good about fostering even when they're at the "annoying" stage. She might chase them a little and "be mean" to them for half a day, but not trying to kill them or run them off or anything, more like a "this is my house, I'm the boss" kind of thing.
We never tried to foster anyone with our third doe.
The does can be extremely territorial. But in general, some don't mind fostering and others won't.
And yeah, they can be finicky. Some can also be absolute sweethearts though, like our third doe Harmony, she's a doll, super docile and lovey.