Anna Michelle, I'm sorry it didn't go well with your dad and this may sound harsh and the main reason being that it is harsh. At least you have tried to keep a line of communication open but once you hit a brick wall, it does no good banging your head and hoping that it will fall down.
The seemingly selfish part is that you have to do for YOURSELF what makes you happy. If they want to cut all ties and end their relationship with you, let'em. Believe me, it will be their loss. They are right, and I assume that you are over 18yrs old, they have fullfilled their obligations to you. They raised you, didn't let you starve to death, clothed you, provided you with love (even if not unconditional now) and so on. It is you now that will have the obligations when they get older and if they refuse to see or accept that and want to cut the ties, it won't be your fault but rather their own. They really need to understand that even though they gave birth to you, your life is your own to live, not theirs.
You can still help them when they are older, even now, and actually you really should. You know all the Karma and stuff. Don't hate them even though you are angry and hurt. Genetic family really don't mean much, it's just a group of people sharing the same genes that you are born into, so their argument about losing family and friends is kinda' weak. You can have family and friends and if they don't accept you, there are plenty of others that will.
It seems to me that you have come to the crossroads and have to decide to go however way you want to follow. If they want to cut ties, let them. Let it be known that it is fine with you. From what they wrote that you posted, it seems to me like threats. Put the "ball back in their court" and say something like "sorry and I really hate to lose the relationship and really can't believe that you can't unconditionally love your own child but I have to go my own way." That would be throwing the guilt back to them and maybe let them see that it is indeed serious.
I have not cut ties with my family in an out and out way because of anger or differing poinst of view and I do love the family that I genetically belong to. But I have also dissappered from that family for years and no one even knew if I was alive or dead because I felt I had to make my own way and live on my own terms unhindered. I've never really felt any obligations to genetic family other than help when they need it and to parents in thier old age. I don't have to agree with them or they me but mutual respect is something all families need to have for one another. Maybe I'm lucky in this sense.
Sometimes you can only talk and do so much. When it starts getting unproductive and the other person/people shut down from trying to understand or start making threats to manipulate you for their own purposes, there's really not a whole lot more that you can do. I won't lie to you, it will hurt and hurt really bad emotionally if they decide to end the relationship with you but it won't kill you. If you need familial support, seek out like minded individuals to share your life with and who will accept you unconditionally because that is what real family is supposed to be about.
What I wrote is in no way right or wrong or what you should or shouldn't do but rather how I would handle the situation. Sometimes we do have to be "seemingly" selfish and live our lives according to what makes us happy with ourselves.
I wish you the best of luck to handle situation. When it comes down to it, be the stronger of the two parties, don't lose your cool. Let them see that you are confident and content with who you are. It may actually concrete the realization to your parents and they may start coming around. You still may have to give them time so be extremely patient. Be ready for whatever happens with whether they do cut all ties with you or want to salvage the relationship. Either way, I wish you the best.