Um, your parents sound controlling and manipulative and literally impossible to please. (Are you in fact my sister?) If they are this abusive, maybe get some counseling?
Having Hispanic parents, but being born in the US I can assure you that this situation is very common. Asking advice from a primarily Anglo group of people, is like asking people of today to judge Christopher Columbus or Thomas Jefferson by today’s standards.
The cultural differences are enormous, and difficult if not impossible for an Anglo to understand the volatile and dramitic emotional response that are actually quite common place in Hispanic families.
The parents believe:
This American boy has negatively influenced their otherwise perfect little girl. She has moved out of the house and is probably living in sin far away from them. They can imagine all sorts of evils, like drug addiction, promiscuity, and other immoral activity. They worry and discuss constantly, with every conversation causing more emotional distress and exagerating the problem.
Why? Americans in general have more liberal standards than Hispanics (in general). Or at least that’s what Hispanics think.

The daughter did move out of the house (which is a huge No - No for Hispanics, until the daughter is married). She has been living alone for 2 years with little communication, and is not yet married or engaged.
Result: Vicious Cycle
Daughter attempts to communicate with parents. Parents are in an emotional, dramatic tizzy, due to many hours of worrying and hyperbolic discussions. Parents vent their emotions by yelling and insults. This causes daughter not to call back; fueling parents’ worrying and dramatic emotional discussion…etc, etc, etc.
Way out? Accept your parents emotional tirades as their way of saying they love you and are worried about you. This is not going to change, as they have been this way their whole life. Rather than fight back, reassure them. I think a letter from bf’s parents, or a visit from you and bf together would be helpful. They are worried, calm their fears, don’t provoke them.
Then move forward with the engagement and marriage. Once you begin to behave like a responsible adult, and get married like a responsible adult; they will worry less, and calm down ( a little).
Hispanics are very emotional. This is great with plenty of good emotions like laughter, and love and optimism, but is terrible with the bad emotions like worry, insults, loss of control and anger. But its a whole package, you can’t have one without the other.
Everytime your parents get all worked up. Imagine that they are a fire – brings warmth but can also bring distruction. What are you? Will you be the kindling wood that adds to the warmth (that is, reassure them, minimize their fears, ignore the negativity), or the lighter fluid that causes an explosion (fights back, insults them), or cold water that puts the fire out altogether (stop communicating, cut them out of your life)?
You can not control your parents, you can only control your response to them.