I have a half-sister I didn't know about till I was in my thirties, and I feel for your daughter, while also understanding more from her reaction why my parents didn't tell me when i was a child.
She's 20 years older than me, and actually was also v easy to find on Facebook once I knew her fairly unusual married name and the fact she had remained in the same area.
I haven't contacted her because I don't know how. There was no adoption, just an estrangement that started when she was in her early teens so registers wouldn't help, and Facebook or social media just seems awful. I have no address, and no real idea what I would say. Yet while I know that she most probably will want nothing to do with me, and I know very well biology doesn't make family- I've close family members who are adopted, ironically- it still feels like a loss. I would like to meet her, once, and see what she's like. If we could have some sort of friendly, adult relationship, or if we're just strangers who share some biology.
My parents viewed it through the lens of everything that had gone before, but for me, it was about a wholly separate potential relationship that had nothing to do with them; the possibility of something that had been taken away from me, and possibly even her, without permission - I have no reason to think she knows I exist. I could not have coped with it as a child I don't think- I would have almost certainly tried to find her as a teen, spurred on by so many terrible films.
So: yes, your daughter should be stopped. But I think you've all been irresponsible in how it has been handled, and I think contact should be made again with his mother to understand a) whether he fully knows his background and b) whether he would be open at any point in the future to any connections, and establishing a way for him to do so, so your daughter can at least be told that there is an option if he wants to initiate it but won't have to deal with direct rejection.
From the mothers point of view, allowing him to be Facebook friends with people who are also friends with his biological father with no warning or thought seems v short-sighted. I think he has to be the priority, but I do empathise with your daughter, who has been given an unfortunate glimpse of someones personal life she has no real right to know about and then told not to ask any more questions.