Which statement is grammatically correct?
A: I am uninterested.
B: Me too./ So am I.
A: I am uninterested.
B: I am uninterested either./ Neither am I.
Which statement is grammatically correct?
A: I am uninterested.
B: Me too./ So am I.
A: I am uninterested.
B: I am uninterested either./ Neither am I.
They are all equally grammatical.
But I think what you are asking about is whether uninterested is treated as a negative polarity word, and so attracts the negative polarity word neither in a reply.
The answer is that it is not so treated, so Me too or So am I is the idiomatic answer.
But there is no other meaning that can be ascribed to Me neither in that context, so it would be understood, but not usual. (Me either is not idiomatic for me in any context).
It’s the first group. “I am X” always takes a positive response. The un- part doesn’t change the verb into a negative.