Reply #7: My guess is they know they're Republicans.

[Philostopher]

They just think their arguments will carry more weight if they attempt to appear to be 'non-partisan' by saying they're not Republicans. Claiming to be 'independent' has long been a way for Republicans to attempt to make people think they actually think about it, but in many cases -- at least here where I come from -- it just means they think it's a stronger position from which to argue for their conservative ideals.

Note -- this may differ elsewhere, but most people in SW Ohio who call themselves independent voters are really Republicans. Your mileage may vary.