I'm an adopted child, so in a way I have a dog in the fight.
Based on my age, my bio parents are probably dead. I know I have 3 half sibs via my bio mother and I'm not sure they know I exist. I would assume that the two older would have known their mother was pregnant, but who knows?
I have no real desire to meet my bio siblings, if I did I would have initiated a search long ago. If they showed up knocking on my door chances are I would shut the door in their faces as OP did, out of pure shock. And the harder they tried to force themselves on me, the more I'd say "No way". Because if someone tries to force themselves into your notice, they're usually someone you do NOT want in your life.
It's just not appropriate nor kind to show up at someone's door and say "Guess who I am!!!!". It's always best to go through an intermediary or via letter. And to realize that if the 'receiving party' to your information doesn't want to know you, you need to accept it with good grace and walk away.
It's up to OP as to whether or not she wants to know the contents of any letter. But the thing is, if these people had written her a letter in the first place, chances are she would have opened it simply because, well, when a letter comes to you, that's what you generally do. But instead they tried to bully their way in, so now the chances are she won't want to read it and will toss it in the bin. Would I read a letter in OP's circumstances? Probably. But my situation is much more straightforward than hers. I have no bad memories of a bad childhood that I wouldn't want dragged up. She does, so her choice is even more important and even more to be respected.
Bottom line is, OP owes them nothing. It doesn't matter who they are, what they want, or what they have to impart. She is not required, morally or otherwise, to comply with their wishes. No one has the right to demand the attention of another person if they want to be left alone, period.