It's a bit of a POV week, with some follow up questions to Monday's post.
Is it acceptable for different characters through whom a story is told to have different degrees of closeness in their POV, according to their importance to the story?Yes, as long as you establish that fairly quickly and be consistent. For example, you might have one POV is first person and another in limited third (Skin Hunger does this), or mix first and omniscient third (the I.Q. series does this), or even change styles per book (The Old Man's War series does this).
However, be wary of what and how many you mix. If you have a lot of third omniscient and third limited characters, it might look like you're POV shifting or just don't know how to handle POV well, especially if the reasons for changing narrative distance aren't clear. Just because you know why one character is less important doesn't mean the reader will, so you'd want to keep the reader's perspective in mind when messing around with POV. Will they understand what you're doing and why?
(More on choosing narrative distance here)
You'd also want to make sure the reason for it serves the story. It's not uncommon to see a distant or omniscient third from the antagonist's POV, but if you have two main characters that seem to be on the same level, then it might feel odd to have one close and one distant without a solid reason.
Also be wary of scenes from random POVs that are there only to show one small piece of information. Like with any POV, if the scene is there just to convey information the main character isn't privy to, you might want to re-think it. POVs that only appear once or twice are red flags for this.
Must that degree of closeness for a specific character always be the same throughout the novel?Technically, anything can be done if done well, but honestly, yes, most folks will advise that you should keep them the same. A sudden change of narrative distance or POV style is jarring to the reader. I remember one literary novel that started out in first person present tense, then shifted to third person past tense for another character, then shifted back to the original character, this time in third person past tense. I stopped reading. It was just too random to keep up with, and the switches made no sense that I could see.
(More on choosing narrative distance in multiple third person)
It's also very difficult to do well, so if you try this, be very careful about how to go about it. Clarity is key when doing anything out of the ordinary.