expressions - Neither do I / Nor do I / Me neither / Me either

In this circumstance, which would be the most correct / natural answer?

Person 1: I don't eat meat
Person 2: Neither do I / Nor do I / Me neither / Me either

This says both "neither do I" and "Me neither" are often used. But I have also heard / read "me either" and "nor do I" in multiple scenarios. Which then is the correct way of saying it? Are the others wrong or just not used?

Answer

It's not a matter of "correct"-ness. It's a matter of social class and personal presentation.

In decreasing order of falutation:

1. nor do I (archaic; now either ironic or intended to sound classy, or both)


2. neither do I (normal in writing, common in speech)


3. me either (common in speech, more familiar)


4. me neither (common in ingroup speech)

... roughly speaking, of course; I'm no sociolinguist.

This kind of social layering for language variation is completely normal, in every language. To call one mode "correct" would be wrong; appropriateness of speech or writing depends on the speaker/writer's aims, and their judgement of their relationship with their listener/reader (and of course on how accurate their judgement is). What's correct in one situation is often incorrect in another.