I think you should move out and act like the adult that you are. Mid twenties--you're a grown up.
No wonder your dad still treats you like a child. You are still living at home, just like you have since you were born. He sees you as the same child you have always been.
And of course your father has the right to set "house rules." He would do the same for anyone who lived in his house. It's his house, right? Is he providing for your other needs besides shelter? Are your parents feeding you? Paying your utilities (electricity, heat, water)? Are they paying for your gas or other car expenses? Are you watching their television? Working on their computer? Storing your stuff on their property?
If you answered yes to any of these questions, then you are essentially still a child, or at least acting like a child, a dependent child, and your father rightfully feels that he must treat you like a child and tell you what to do and who to do it with.
So act like an adult and take control of your life.
If you can't get a full time position, then work at several part-time positions to earn enough money to proide for yourself, and live very simply, with no luxuries. (Hope you like Ramen noodles--the staple food of young adults living on their own!)
I hope that you own your own car at least--many high school students buy and pay for their own car by working at McDonald's. If you don't own a car, hopefully you live in a city where you can use public transportion, or live in a city warm enough to bike or walk to your various jobs.
While you are working at part time jobs, keep applying for full-time positions in the area that you majored in, and hopefully, you will eventually land a good full-time position that pays a really great salary. But don't wait until you find that perfect job to move away from your parents. Move out now.
You probably won't be able to afford a place by yourself, so find yourself some roommates, just like lots of men (and women) have done through the decades. Usually when three or four guys all chip in, they are able to afford an apartment or a rental house. If you don't have a lot of money to chip in, you might get stuck in the smallest bedroom, or in the basement, or even end up in a corner of the living room with a curtain between you and the rest of the apartment.
But you will be on your own, living as an adult, no longer under the authority of your parents. And you can live your own life, make your own decisions, and do what you want to do with whoever you want to do it with.
I don't believe that your parents will break off all contact with you if you move out. Parents expect their children to grow up and move out. They may experience the empty-nest, and be mad at you for making them face that fact that they are now getting older. But if they have loved you all of your life, they won't stop loving you because you do what all humans do--grow up. They'll eventually recognize that you are an adult man.
I think what they meant when they said that they will have nothing to do with you is that if you move out, they will not provide for you anymore, or pay your bills, give you money, buy your gas, or bail you out of emergency expenses. And that's good and right. If you move out, but your parents are still paying for your expenses, then you're not really a grown up, and you're being a dreadful financial drain on them, and I don't blame them for not wanting to get into that burdensome situation.
Good luck to you. I know you can do this.