Using and losing 'the'

Whenever you use ' the ', it means that you try to specify the particular thing or person and has a sense of making comparison.

" The people in my country always vote ( the ) Republican. " means ' other people in their country might not always vote their Republican '

So, I think using ' the ' is not necessary in this sentence, I go for the first without it. But ' the ' for Republican is necessary since it singles out ' this ' unique party among others.