I can't speak for hardcore political types who have to warp everything through their ideological lens, but when I saw the CA: the Winter Soldier (which I only saw at the insistence of a friend of mine and was surprised that I did enjoy it as a popcorn flick), I didn't see Hydra as Republican. My understanding is that they'd have agents in both major parties, and also among those who spoke out against both major parties, and would have them among law enforcement and terrorists both. That Captain American and friends worked for SHIELD strikes me as Homeland Security, and HS strikes me as more Republican than progressive, and as was shown, there were heroes and villains both in the agency.
I'd see the politicians the same way, some would oppose Hydra, others would be secret agents of it (and they'd have to be secret because otherwise they'd be drummed out--granted, secret Hydra agents would be among those to drum them out, but only to protect their own secret and thus minimize the damage to Hydra's assets, heck, Hydra agents could frame someone else as being with Hydra, that sounds right up their alley). Hydra is a conspiratorial organization that remains in the shadows, and according to the movie they'd given up in trying to convince people through either conversion or force, but rather to manipulate people into demanding their dominion in the guise of the fronts that already exist which Hydra has secretly infiltrated (in which case they'd probably still stay in the shadows using their various front organizations on both sides of the law as convenient). To think that Hydra could be identified by party affiliation strikes me as silly since that would defeat the entire point of Hydra.
As for Hydra succeeding so well so that they took (momentarily) full control of SHIELD in
CA: The Winter Soldier, that's just standard storytelling, and plenty (like the X-Files) are even based on it (the exception is when the threat is so vast that the government itself becomes beleaguered, such as in the movie Independence Day). There's got to be a reason why you can't just call the authorities, and/or for the heroes of the story to stand on their own (happens in Buffy and Angel quite a bit as well). It happens everywhere, it even happened in the Star Trek series (from the episode
Conspiracy to
Section 31 to the movie
Insurrection ), but that's hardly a political agenda at work, just an old way to tell an exciting story where the heroes shine.
Just thought I'd add, whether intentional or not, Captain America (in what little I've seen of him, from CA: The Winter Soldier to Avengers) makes me think of someone who strongly missed the speeches of JFK, which would make sense. And JFK would be very out of place today with his speeches that were thoughtful, compassionate (but not touchy-feely), and respectful. That is, I don't mean he'd be out of place for his views, but more for his attitude and appealing to the better parts of humanity rather than the lowest common denominator (often with rhetoric as shallow and meaningless as a bumper sticker slogan) as seems to be the case today (at least in the USA). Both Captain America and JFK (given what I've seen of both) just couldn't fit into the modern system today.