Of the first two sentences, 2) is the one you would hear more frequently. It is informal and is correct:
"¢ It is you that is (that's) crazy.
Of the second two sentences, 2) is also the one you would hear more frequently. It is informal and is correct:
"¢ It is not you that is (that's) crazy.
A passage from Quirk* about cleft sentences states:
"In relative clauses and cleft sentences, a relative pronoun subject is usually followed by a verb in agreement with its antecedent. It is I who am to blame, It is Kay who is in command, It is they who are complaining.
But 3rd person concord prevails in informal English where the objective case pronoun me is used. It's me who's to blame.
Similarly, 3rd person singular may be used in informal English in these constructions when the pronoun you has singular reference: It's you who's to blame."
So, in a formal tone, the sentences would be:
It is you who are crazy.
It is not you who are crazy.
Informally, the sentences would be:
It is you who is crazy.
It is not you who is crazy.
Quirk does not address "that" as a pronoun to refer to persons in this section on cleft sentences, but others do. Michael Swan**, for example, has these sentences:
"It was my secretary that sent the bill to Mr. Harding yesterday...
It wasn't my husband that sent the bill....
...Who is possible instead of that when a personal subject is emphasized...It was my secretary who sent the bill.
When the emphasized subject is a pronoun, there are two possibilities. Compare:
It is I who am responsible. (formal)
It's me that's responsible. (informal)
It is you who are in the wrong. (formal)
It's you that's in the wrong. (informal)"
As for "It is you that are" and "It is not you that are," this construction exists but less frequently than the others. There are only 690 examples of affirmative constructions on Google, like this one, written by novelist Henry James in 1880:
"¢ Washington Square by Henry James. Tools and Options, ... "I call this a scene.". "It's you that are making it! I have never asked you anything before. ...
There are 393 examples of negative examples, like this:
"¢ to technology and new ones appear. Remember, it is not you that is redundant it is your job. In the previous article we discussed ...
jobs.financialdirector.co.uk/Features/1154765 - 36k
There are 1680 examples of "it is you that is":
"¢ Most of all, it should be about respect for you, the internet user, at the end of the day, it is you that is losing out, and it is you that these people are ...
There are 48 examples of "it is not you that is":
"¢ ... If there are a lot of these hops they can get lost on the way. Doesn't help you connect, but at least you'll know it's not you that is the problem! ...
In contrast, "who" is the relative pronoun used more frequently in cleft sentences to refer to persons:
There are 245,000 examples of "it is you who are":
"¢ "It is you who are mistaken, about a good many things". On
the Phantom Menace, and other title musings. In the months ...
There are 662 examples of "It is not you who are":
"¢ He wrote to her. ˜It is not you who are influenced by me; rather, it is I who am influenced by you.' People quote Ustvolskaya; she does not quote them. ...
There are 30,300 examples of "It is you who is":
"¢ ... I think it is you who is wrong. "Nobody buys Windoze today or tomorrow!" What? No one buys Windows? How stupid of a statement is this? ...
There are 662 examples of "It's not you who is":
"¢ ... to deal with. Second, he is a bully, abusing his power over you. It's not you who is making him into a bully. However, it is important ...
There are other ways to phrase your sentences in order to avoid discomfort about this grammar point. You could say:
You're the one who's/that's crazy.
You are the person who's/ that's crazy.
You're not the one who's/ that's crazy.
You are not the person who's/ that's crazy.
*A Comprehensive Grammar of the English Language, by Quirk Greenbaum, Leech, and Svartvik. Longman. 1985
**Practical English Usage by Michael Swan. Oxford University Press. 1995