I'll gladly give my two cents on this question, but bear in mind that I've been doing everything possible in the last little bit (particularly the last few months) to avoid most news. I realize this isn't good practice for a citizen, but all it does is make me angry and doesn't persuade me of anything I didn't already think. This is a brain dump, so may be a little disorganized.
Anyway, for my part, it's similar the way I hear a lot of people from elsewhere talk about the U.S. There's a recognition that the government doesn't necessarily speak for or accurately represent the people as a whole. Besides which, a large, heterogenous nation like Russia (again just like the U.S.) isn't going to just have one unified feeling on much of anything. Plus both countries are guilty of much of the same stuff.
I find Russia's foreign policy more than a little scary. I've seen it argued on more than one occasion that Putin's idea of success is just to fail more slowly. There's certainly a stereotype of Russians as (not undeservedly) gloomy and pessimistic, and that can certainly come through in some governmental actions, even if it's not been my experience of meeting actual Russians face-to-face. I also think there are just plain some different values there, which is to be expected (and I don't pretend to know Russian culture especially well). What little I do know makes it seem more traditional than the U.S., and that it does trend towards more group-oriented than individualistic like the U.S. This isn't a bad thing per se, just depends on how it plays out. Anyway, with foreign policy, Russia's coziness with some shady regimes only makes sense through this "failing more slowly" narrative, especially in the case of North Korea and Iran.
I also see maybe a little bit of an inferiority complex in the Russian leadership. The USSR was one of the two superpowers, although there's some question about whether that was actually true. Just as no one on the outside is truly sure of what kind of shape the Chinese ecnonomy is really in, something as centralized as the USSR could cook the books pretty easily (and certainly had more than a few incentives to do so). Now, though, some of the cracks are showing: the few signs of poor maintenance in the military that have made the news (e.g. the Kursk and the need recently to send the россиский флот's only nucelar aircraft carrier back from the Mediterranean), and the tough time the Army had in Chechnya.
This is what I see as leading to some of the uglier social issues too, like the crackdown on homosexuality. I have no reason to think Russians are innately more homophobic than the U.S. is, but minorities of whatever type are a good distraction from the leadership fucking up the place. (I don't know if the скинхеды are still as big of a problem as they were, but I'd put that in a similar category.) Again this parallels what we're seeing in the U.S.; Republicans would gladly do the things Putin is doing on the social front if they thought they could get away with it.
I remember an interesting conversation I was part of back in 2004 or so with Юрий Шевчук (founder of ДДТ). He was definitely anti-Soviet and anti-authoritarian in general (I remember he was in Kiev when the anti-Yuroshenko protests were happening). Aside from a pretty fascinating story about playing a show in a stadium in Grozny during the ceasefire that was attended by thousands of soldiers from both sides, his perspective on the state of Russia at that time was that the time spent in such a tightly-controlled system meant that suddenly people had much more freedom but didn't know what to do with it. In other words, there may not have been the cultural support for a more democratic setup. I think this is an underappreciated aspect of what's required for a representative system, and is why Trump is so dangerous.
The few Russians I actually met, mainly during college, were some of the warmest and kindest people I've ever known. I still miss terribly one Moscovite, Рамил, whom I used to hang out with during his semester at my school. I loved how much more open the Russians I've known tended to be; sometimes it could almost seem blunt to American sensibilities, but I liked their willingness to both express emotions more readily and to simply cut to the chase and not dance around. And as is common with people from parts of the world that have had a rougher time of it, they tended to have this innate sense of joy at life just in general (my theory being that if the outside world sucks, you have to find that sense of happiness somewhere inside). I also had a really cool opportunity (that I want to punch my younger self for not taking further advantage of) to meet some much older Russians at a local retirment home. There were even a couple guys there who had been in WW2, and they all enjoyed talking to us even with our pitiful Russian. There was also one grandmother I was talking to who introduced me to her frightfully attractive granddaughter...who turned out to be like 14 ><.
Turning back to the broader question about the attitude towards Russia generally, I think it's less a case of outright anger or hostitlity towards Russia and more just a recognition that an outside group (in this case a country) who doesn't necessarily have our best interests at heart tried to fuck around with our election. That it's Russia doubtless still carries some baggage from the Cold War, but to an extent I think most of us recognize that it's the kind of crappy thing that countries tend to do to each other (and God knows we've fucked around in others' elections often enough over the years). Even more than this, though, it's become an internal political thing: it's more about a way to discredit (and hopefully get rid of) Trump than it is some broader existential threat. I haven't seen any particular calls for retaliation or anything like that. I actually think this means that the extent to which Russia actually influenced our election is being overblown, since again it's a line of attack on Trump. We have no shortage of those, but this is the one that might have some legs (although if anything does him in, it'll be the cover-up rather than any actual collusion IMO).
So broadly speaking, I'd say we see Russia as a rival but not an enemy. We condemn some things (the gay rights issue, the invasion of the Crimea, etc.), but no one is burning Russian flags or anything. We definitely see Putin as a corrupt autocrat, but the world is hardly short on those.