I’d try to be conciliatory and say I wanted to talk about with her as any two adults
would. As everyone says, no, you can’t choose for her, and if you decide you can and will, and push too much to stop the friendship it might make her secretive, or worse, more likely to move in with Vicky. But it’s absolutely your role as her mum to a young adult to be a resource, a source of comfort and a support. It’s fortunate you’re familiar enough with the organisation to have not simply treated it as a joke.
Is your daughter already aware of any of the quoted information, or your specific concerns around dangerous messaging (re:suicide)and extremist associations?
How did she respond?
If she were my DD I wouldn’t treat this differently from any other concerning influence; I’d lay out what was worrying me, without personalising it to Vicky, using a few select pieces of the most credible, independent source material I could find, ie. not a repudiation by the church, or anything similar, good investigative journalism from broadsheet newspaper articles, reputable academic journals, that sort of thing. I’d do that so I could be clear that these are serious points to be considered, not just nasty rumours or religious prejudice; speaking as an atheist (who dresses entirely in black (side note: being edgy in black is not particularly persuasive evidence she’s about to convert to Satanism, she may simply appreciate the aesthetic)) having a child living in a house with someone with these beliefs would potentially concern me too.
I also wouldn’t juxtapose this information against your own religious point of view, or present it as a fait accompli that having considered this information she must stop being friends with Vicky. Haily is an adult and entitled to form her own views and beliefs, just like the rest of us. Vicky is also entitled to her beliefs, however, as with any controversial belief system with some uncomfortable associations, it’s totally feasible you’d have concerns. It might have been easier to either allay/support those concerns if Vicky hadn’t been banned from your house, so maybe that’s worth considering as well.
You seem fairly well informed so hopefully your daughter is of an enquiring mind too, and of strong character. Also, are you totally sure this goes beyond the sartorial? It’s not inevitable that we all follow our friends’ religious beliefs, they’re quite personal, no? What if Vicky has no interest in bringing Haily into her church (do Satanists proselytise?)?