So, I don’t read the comics. All I know is the movies. And I saw them out of order. Iron Man first, then The Avengers.
Given that, was it obvious before Avengers that Hydra infiltrated SHIELD? How far back in time? Were they there when Old Man Stark prefected the Super Solider syrup?
And to my primary question - has all Hydra influence been purged from SHIELD by the time of Infinity War? Does SHIELD still even exist?
Basically, it goes like this:
So yeah, basically Hydra was there from SHIELD’s founding.
In the movies, SHIELD is no more, but Nick Fury appears to have created some sort of new independent group. It’s not clear what they are, but we’ll probably learn more about it in Secret Wars. There’s at least some Hydra remnants still out there. One shows up in Ant-Man and stills Pym Particles at the end.
Now, in Agents of SHIELD, which is unclear how much is canon to the show, SHIELD gets destroyed and reformed multiple times. They’ve also wiped out Hydra multiple times, but like the saying goes, cut off one head and two more grow. They supposedly destroyed the last cell shortly before the events of Infinity War, but that appeared to take place in an alternate timeline.
Shield didn’t exist yet when the Super Soldier Serum was created - it was formed after WWII. Hydra was infiltrating other organizations before that - the spy who tries to sabotage the creation of Captain America, for example - but not to the extent that they were later able to compromise Shield.
Shield itself was apparently compromised from the beginning. After the war, when Shield was being formed, they brought in “ex” Hydra agents who had valuable knowledge like Armin Zola, Operation Paperclip style. Presumably, it took some time for these agents to exert control over enough of the organization that they could pull the coup we saw in Winter Soldier.
When you ask how obvious it was, I’m not sure what context you’re asking in. Do you mean “How obvious was it to the characters in the story?” Or “How obvious was it to the audience at the time?” Although, in both cases, I think the answer is “not very.” Nick Fury, arguably the best spy in the world, only had vague suspicions that something was off in his organization, and I don’t recall any hints dropped in previous movies to suggest that such a betrayal was in the cards.
After the events of Winter Soldier, Shield was officially disavowed and defunded. At the end of Age of Ultron, a heli-carrier showed up to help evacuate Sokovia, which was established in the TV show Agents of Shield as being the results of Shield reforming and getting it’s shit together, but the show is mostly non-canon, so it’s not clear if that was still supposed to be Shield, or what. The end credits scene on Captain Marvel showed that Nick Fury is running a new operation, apparently in outer space. This is likely Sword, a counterpart to Shield from the comics that focuses on extra-terrestrial threats.
The MCU seems largely finished with Hydra as a major threat, so I think it’s safe to assume that they’ve not infiltrated Fury’s new org.
Spoilers for WandaVision:
In WandaVision, we see the MCU version of SWORD, and it seemed pretty clear to me that it’s a completely different organization from the one Fury now appears to be running. Fury’s operation, from what we’ve seen of it in credit cookies, certainly seems likes its inspired partly by the comic book version of SWORD and partly by the 2015+ version of the Ultimates. I suspect we’ll find out a lot more in the upcoming Secret Wars, and probably also The Marvels.
FTR, the upcoming show is Secret Invasion, not Secret Wars. Secret Wars hasn’t been confirmed as an MCU project, and probably won’t be on the radar for a few more years.
The HYDRA reveal in Captain America: The Winter Soldier came completely out of left field. There was no internal evidence I’m aware from the movies prior to that setting any of it up. HYDRA appears in Captain America: The First Avenger, and then only gets a couple of passing mentions as something that existed in World War II. There were some hints in Marvel’s Agents of SHIELD that HYDRA still existed in some form, but not that it had infiltrated SHIELD, and that show was only ever in loose continuity with the MCU, anyway.
And SHIELD as portrayed in CA: TWS seemed to be retconned a bit to fit HYDRA in. From what we had seen previously, Nick Fury was SHIELD director, and answered directly to a “World Security Council”. Yet in CA: TWS, suddenly there’s a never before mentioned or alluded to “Secretary” of…something, who’s Nick Fury’s boss (and secretly a HYDRA agent).
I personally doubt there was any sort of plan prior to CA: TWS to have SHIELD wind up being a HYDRA front and being totally destroyed. Among other things, it literally blew up the premise of Agents of SHIELD half-way through the first season. It really had the feel not of a carefully coordinated and planned story, but more of “well, we’re supposed to be in tight continuity with the movies, and have tie-in episodes every time one comes out, and now the latest movie just totally blew up our premise, so…I guess we’ll try to deal with that somehow?”
Right, sorry, that’s what I meant.
That one.
I know there are a lot of hints and easter eggs in the movies that go right past me. I’ll be forever lost trying to fit the movies into comic canon. I just take the films as they come. As long as it isn’t required to know the comics, I’ll be OK. 
So it’s funny - SHIELD did it to itself. From the beginning they were compromised, even in Thor and Avengers . They were really never actually “the good guys” at any time, more or less. Only so much as SHIELD goals didn’t conflict with Hydra, or operations Fury was personally in charge of.
eta: was the plan to have air-based weapons platforms that could (would?) kill nearly everyone a Hydra plan, or a misguided SHIELD (what could go wrong?) plan?
The SHIELD plan was to have a network of airborne weapons carriers - helicarriers with big guns - in case of, oh, say, alien invasion, or an invasion by Dark Elves, or super villains running amok, or robots running amok, or remotely-operated power armor suits running amok, or wizards running amok, or any of the other global crises we’ve seen in the MCU. HYDRA’s plan was to piggyback on that program to use the platforms and advanced AI to preemptively target and kill anyone who the AI predicted might be a threat.
It would have targeted threats to HYDRA itself, but also criminals, terrorists, and the like, anyone the AI says is a threat to global security and stability. But also, probably, political dissidents, protest leaders, and others who might upset the status quo. HYDRA is, in its own twisted way, trying to make the world a better place.
Nick Fury and the other “true” SHIELD agents are horrified by HYDRA’s corruption of their plan, and with barely a moment’s hesitation take the fight to the HYDRA agents and try to help Cap take down the helicarriers.
I’m pretty sure they knew where the MCU was going SHIELD-wise at the start of the first season. That’s why the first half of the show kinda sucks, because they’re basically just spinning their wheels wait for the big shake-up.
And here’s the article about how they knew all long and had to plan for it:
Well, the thing is, and I think I’m in a minority on this, I actually liked the first half of the first season. It was exactly what I wanted from an Agents of SHIELD show, and it didn’t feel at all to me like they were spinning their wheels. On the other hand, in the back half of the season, it seemed a lot more to me like the writers and show runners weren’t quite sure where to go, and from the second season on it felt to me like they were flailing, and didn’t know how to make an Agents of SHIELD show without, y’know, SHIELD.
I really didn’t get the impression that the show was designed from the ground up with the idea that their whole premise would get blown up half-way through the first season.
Yeah, I agree. It felt like the first season finale was the only idea they actually had when they conceived the show - “Let’s setup a character as a hero, then reveal he was a villain all along when WS comes out.” And then they didn’t have anything to do until they got to the end of that season.