Issues :-
1) placement of prepositional phrase "of Indiana" next to what it modifies - ' the ceremonial state flowers'
2) Neither and either are preferred with SINGULAR verb, so IS is correct.
The ceremonial state flowers are of Indiana, the peony, and of Vermont, the red clover, but neither are native to North America.
A The ceremonial state flowers are of Indiana, the peony, and of Vermont, the red clover, but neither are
Both modifier and verb issueB The ceremonial state flowers are of Indiana, the peony, and of Vermont, the red clover, but neither is
Modifier issueC Ceremonially, the state flowers are the peony for Indiana and for Vermont, the red clover, but neither are
placement of ceremonially changes meaning..
Parallelism in two parts joined by AND
Verb issueD The ceremonial state flower of Indiana is the peony, and that of Vermont is the red clover, but neither is
CorrectE The ceremonial state flower of Indiana is the peony, and the red clover in Vermont, but none is
parallelism issue ...
Neither is better than noneD