Yes, they can, but there is a limit. Someone who is say a billionaire being genuine friends with say a lifelong homeless person isn't generally going to be possible because it inevitably leads to the question of who would let an actual friend live on the street like that when it would be a trivial act to change things. That said when it comes down to questions of "poor comparative to the rich guy" that's something entirely different, someone who is say middle class and pretty well off overall, having a decent house they are in no danger of losing, a fair amount of spending money, a decent car, etc... having a friend who is a multi millionaire or even a billionaire is a different matter entirely. When it becomes more a question of relative creature comforts as opposed to a basic state of living it's not that much strain on a relationship.
Of course it should be noted that there is more to this than simple economics as there are different types of rich people with different perspectives. For example when you start dealing with "Old Money" families that have been rich for generations there tends to be a very different mentality from say "new money" who are people that got rich within a generation or two. Old Money tends to be concerned with dynasties and holding onto what they have a lot more than those with more recent fortunes, as they literally watch other people with fortunes come and go. They tend to want to keep their relationships, marriages, etc... within very select groups of other old money families so as to reduce the odds of losing their money and oftentimes property, as it can literally take one bad marriage to decimate a fortune that might be a hundred or more years old.
The "Old Money" types are the ones people most think of when they look at snooty rich people, but to an extent there is some justification to the attitude which you can see when you look at what happens to fortunes every year, especially with some of these billionaire party boys who made their fortune during say the .com boom and then squandered it all.
If you were to ask me I'd say that no, a poor, or comparatively poor person can't really be friends with someone from "Old Money" and raised within that world. When it comes to newer money though, it's less of an issue and there tends to be less paranoia. On a lot of cases when it comes to celebrities and the like you see a lot of friends and family in their entourage for example.
As far as the whole Marine Antoinette thing goes, that's a very unique kind of situation that goes beyond even "old money" logic since she was the queen of France. Royalty/Nobility/Peerage can all come with an entirely separate set of logic and rules, in that case your not just looking at finances, but also politics, international relations, and both preserving and spreading blood lines. While history has recorded her as something of a twit, I don't think Marie Antoinette was all that bad, mostly having been smeared by out of control socialists who were pretty much cleaning house of their rivals and the opposing government/royalty. The initial leaders here being so out of control that eventually they themselves were put down like mad dogs although by that point the damage had been done. Her whole "let the eat cake" thing and lavish spending was mostly portrayed the way it is because of the explosive class divide, she mostly just acted like a Queen, which she legitimately was, and what's more she had a lot of her own money from Austria, so she wasn't entirely spending from the Crown's coffers, her marriage to the king arguably having brought far more money into the purse than she was spending which was part of the point. That said acting like your a queen when your not is kind of obnoxious, and in all seriousness while "Old Money" can be arrogant they usually don't take it that far, in many cases what seems to be looking down on people is more a matter of isolation and tending to their own affairs. If you ever follow the so called "Society Pages" you'll sort of get the idea. Part of the fascination with Paris Hilton and Nicole Richie is that they are effectively "old money", and are out in society and a lot more approachable (or at least visible)than a lot of similar people, when most people who are connected to things like the Hilton Hotel fortune tend to keep a relatively low profile.