In what dialects is "I don't like it too" grammatical?
Solution 1:
That particular instance shouldn't be construed as a negative clause for the purpose you suggest.
Imagine there's no countries
It isn't hard to do
Nothing to kill or die for
And no religion too
In this case, the "too" is part of an enumeration of things Mr. Lennon is asking you to imagine.
To phrase it another way, imagine that there are:
- no countries (it isn't hard to do)
- nothing to kill or die for
- and no religion too.
More abstractly, then, imagine A, B, and C too. That the contents of C may be negative doesn't affect use of too.
Addendum
Note that this also applies to the following:
I don't like it.
I don't like it too.
You would certainly have no objection if we reworded slightly, still using the word too:
I don't like it.
I too don't like it.