I see a lot of stuff about scamming in EVE and how it's allowed by the developers. How can I find trustworthy people to play with? Secondly why do they allow this sort of griefing activity that would get you a rapid ban in other games?
I have never played EVE myself, but know a few people who do. As such, take my advice at face value.
Finding trustworthy people to play with while in game is difficult. If it's at all possible, convince your real life friends to play with you so that you start out with people you can trust. If not, hopefully you have friends from playing other games. Convince them to play EVE with you. Barring that, I'd suggest trying to play EVE on your own and carefully approach other people until you can determine their trustworthiness.
As for your second question, the developers of EVE have turned it into a bit of a social experiment - seeing what players will do to each other given minimal moderation. Notably, last year's Burn Jita event provided a lot of insight into human nature. At this point, it is littered with trolls and griefers. If that doesn't sound appealing, I'd suggest avoiding EVE entirely.
To me, this question boils down to, "How do I find trustworthy people in life". This process is probably something you do every day in your life. You meet people and depending on your interactions with them, your opinions and trust level with them are affected. EVE is widely known as a game with almost no rules. You wouldn't trust someone you just met enough to loan them money out of your bank account in the real world, and you shouldn't in EVE either. So to answer your question more directly, get to know them, play with people and talk to them, build a rapport.
And to your second question, CCP wants EVE's universe to be as realistic as possible. There are bad guys in real life, and the same can be said for EVE.
Play with people you know from outside the game, that is the easiest way to find trustworthy people. Of course that is not always possible.
Don't trust any member of Goonswarm Federation if you don't belong to them yourself.
Don't pay upfront for anything if you don't know the people involved. E.g. don't pay if a corporation says you have to pay a fee to become a member.
Start in a newbie-friendly corporation like EVE University, they are reasonably trustworthy. There you can meet some players and get a feel for the game and where you have to pay attention to avoid being scammed.
And remember, as a new player you don't have much to lose. Even if you get the occasional ship blown up or lose some money because someone took advantage of you, it's not the end of the world.