If you are social, if you are smart, not a selfish asshole... people will like you, accept you, and most people realize that we don't pick our parents -- how much money you have in college doesn't matter. Going to an Ivy... it's not the academics that sets the alumni apart, it's the networking. You learn to judge your peers based on who has potential and who doesn't -- this is the elitism that a lot of people talk about. Some of that is based on money (clearly a kid who has billionaires for parents has a leg up), but a lot of it is based on the individual person. If you feel like a lack of money will hold you back... then it'll hold you back. If you don't... it won't.
So how this plays out... mind you this was 20 years ago... but in my fraternity (which wasn't one that asked for parents' financial records) we had a checkbox on the form you turned in along with your dues, and it simply said, "I can't pay my dues this semester." I don't recall anyone scamming the system, and it was in place because we didn't want to discriminate against brothers who didn't have as much money, or who were going through a rough patch. I remember talking to a guy who had come to a bunch of our parties... he was dead set against rushing... I pulled him aside 1:1 and asked if it was a money thing... once we got past that he was in and became one of the officers a few years later. (I probably wouldn't recommend everyone join a fraternity, but they can offer a sort of extended family / support structure that's nice when you're away from home for the first time.)
Another example... I had a weekly poker group... we started off playing for $20 in chips. We would invite people based on who we wanted to hang out with, smoke cigars with, drink with... and someone ended up bringing his roommate. Cool guy, we all loved him. He said he didn't have $20 to spare. Rather than just give him $20 (which would have solved the issue but made him feel like he didn't belong or was beholden to someone else) we just dropped the entrance fee and played for chores. 5 guys... The winner got 2 chores from the person in 5th place, and 1 from the person in 4th, and 3 from the person in 2nd. And similar allotments... I had to vacuum that kid's apartment and do his laundry after he beat me (and he had to do the same for me when I won). If you wanted to "buy back in" you could, but it cost you some outlandish dare... basically everyone would get to humiliate you in exchange for more chips. In the end the money wasn't at all important, we were still all just playing for pride.
Final example... Textbooks have always been a bitch. Even 20 years ago. I'm sure it's worse now... but back then we'd line up classes with friends, form study groups (typically these transcended semesters), and then we could buy one book for 2-3 people. The added perk of this was we could share notes, do less work... cultivate that whole networking thing that was so important. If you were smart, took good notes... everyone wanted you in their study cluster. You could negotiate... if you had money or not... "Let's do this, just the 3 of us... I'll take notes 1/3 of the time but I don't want to pay for the book..." and the guy who took sloppy notes would say, "Sure, but how about you take notes 2/5ths of the time and I'll buy the books..." And anyway I remember a lot of people having little deals like this.
Is every school different, sure. But I think it all goes back to internal perceptions. If you define yourself as ugly and fat... you won't get a date. If you define yourself as stupid and slow... you will get bad grades. If you define yourself as poor or struggling... life will be hard. But if you can just not think about that stuff... then you realize that nobody else cares about that stuff either. We're all too busy focusing on our own shit and own insecurities to worry about anything you have going on in your head.