The bottom line is if your over 18 years old you can do whatever you want ..
But you have to be able to take care of yourself if you want to move out , don't expect your parents to pay your bills .
Maybe your parents have a point on your b/f how old is he ? Have you ever met him in person or just on line ?
Have you done a background check on him ? 'knowledge itself is power and you need to know if this guy is shady or not but the only way to find out is checking on his history . and if he gets set for you to ask him then he is hiding something .

Parents want the best for there kids and if this guy has bad credit and owe's a lot of money then I agree with the parents .
Last thing you want is to end up messing up your credit score , you will have a hard time buying anything like a car or a house in the future .

Can you just move out but not live with your b/f ?
Your future really depends on your choices now .