"me too" is idiomatic, even in cases when "me" is technically the subject, and there's little point analysing it beyond that. In response to "I love you", the only idiomatic response, of the options you have presented, is "I love you too".
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Anonymous Is "Me too" grammatically correct?Yes. The argument is often made that the so-called subject forms are really not subject-forms at all, but forms that occur before a finite verb. The so-called object-forms are then used for all other situations, so the argument goes.