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Is conversation grammatical?

Grammatical meaning, the way an essay and academic writing is. What is the basis of your position.

Thanks.

Conversation should be grammatical, but depending on the other participants, idiom, colloquialism, slang and contractions are often included.

Rules for writing, especially for academic work, are stricter than for casual conversation.

Shoo nu-ff. Like every time I quote Shakes-pear I say quote Macbeth Act 3, Scene 2 end quote!

Grammatical to a certain extent, but NOT the way an essay or academic writing is grammatical.
Essays are static.
Conversation is change and movement and flux.
People don't converse in complete sentences, but in sentence fragments, sometimes single words or phrases, constantly interrupting one another.
This is not to say that one may feel free to use double negatives in conversation, but that has more to do with comprehension than it does with strict grammatical rules.