What is the difference between “they” and “it” for people, especially for those people who identify as non-binary?

Indeed, it is rude to refer to a person as "it", which is the pronoun for objects and animals (except sometimes when the animal's sex is known). You shouldn't use it for people.

Singular they (though not universally accepted) has a number of uses:

• Talking about a generic or unknown person: "Will the owner of the blue car turn off their lights?"
• Talking about a person you know that the other person doesn't, whose gender isn't particularly relevant: "My friend, they were at the store this one time..."
• As a personal pronoun. It is widely used even by people who aren't non-binary: for example, people who take up they/them online for anonymity or to not have their gender influence how people perceive them.

On Writing SE I evaluated different pronouns that can be used for a non-binary person. Here's the relevant section on it:

It is the pronoun used for inanimate objects and animals (usually, though even animals are given gendered pronouns when known).

Polls (gender census) indicate that some people want to be referred to as it, though I have never seen this, ever. However, referring to a person as it is almost always intended as an insult, an insult I’ve seen used specifically to make real-life trans people feel less than human.

In the media, the same trope is used over and over again for the same purpose: "It" Is Dehumanizing (there are many, many examples, most of which have nothing to do with gender identity admittedly).

Note:

• There is a grammatical construct that makes it look like the pronoun it is being used as a person's personal pronoun. It's not. Compare "it's Andy" with "it's me", "it's you", and even "it's Harry and Glenda". It's called "dummy it", which is also used in "it's raining".
• There is one time it's ok to refer to a person as it, and that's when it's a baby. But when you do know the sex of the baby, it's customary to use the appropriate gendered pronoun. (Though a very small minority of people have decided to just use they/them pronouns for their child from birth, until the child can decide what pronouns to use.)

In English, different pronouns are used depending on the animacy of what is referred to. There are three cases:

• People are referred to using "he," "she," or "they" (or sometimes using invented pronouns).
• Inanimate objects are referred to using "it."
• Animals may be referred to either way. If the speaker thinks of the animal as being like a person, then they will usually use "he," "she," or "they." On the other hand, if the speaker thinks of the animal as being like an object, then they will usually use "it." People usually refer to housepets as "he" or "she," but they usually refer to vermin and pests as "it."

Referring to a person using "it" is offensive and extremely rude, because it implies that the person is vermin or an inanimate object instead of a true person.

Why is there a distinction between pronouns referring to people and objects? It's simply part of the meaning of those words. Part of the meaning of the words "he" and "she" is that the thing referred to is a person (or animal), not an inanimate object. Likewise, part of the meaning of the word "it" is that the thing referred to is an inanimate object (or animal), not a person.

If you don't know a nonbinary person's pronouns, then you should definitely refer to them using "they"; referring to them using "it" would be extremely rude.

(Of course, as GArthurBrown points out in a comment, there are a lot of common phrases where the word "it" seems to refer to a person. The examples he gave are: "Who is it?" "It's Joe?" "Oh, it's the guy from the auto shop." "It's a boy!" The way that I would think of these sentences is that the word "it" refers not to a person, but to a position that a person is in, such as "standing on the doorstep," "calling me on the phone," or "newly born.")

You will still, rarely, hear people call babies “it” without any negative connotations. This is a vestige of the Old English word for child having once been grammatically neuter, and was more common in the past. The King James Bible does this sometimes (“Take this child away, and nurse it for me ....”) and so does Shakespeare (“If ever he have child, abortive be it, prodigious, and untimely brought to light, whose ugly and unnatural aspect may fright the hopeful mother at the view ....”) A quick Web search turned up current examples like, “Parents with a new baby are almost always asked, ‘Is it a boy or a girl?’”

I’ve never heard of anyone requesting to be called “it,” but I suppose someone eventually will, to be different.

If a non-binary person is introducing themself to others, they will state their pronoun. And if you're not sure of someone's pronoun, you could always ask them — it's just as socially acceptable as asking someone their name.

IME non-binary people's most frequent choice of pronoun is "they". Some choose a neo-pronoun. I don't know anybody who prefers "it".