I was clear with dc that our decision was dependent on factors relating to their age and the length of their relationship. So:
When dd was 16, and her bf was 15, we said no.
In their late teens / university age they could stay together if they'd been together for 6 months - however that meant 6 months after WE had been introduced to the boy/girl friend (to avoid the lie that they'd been together for ages but that we'd not known about it, and to ensure that I met any potentially serious boyfriends early on [nosy mother emoticon])
I can only imagine that if they were late 20's and brought a new partner home, I'd rely on whatever they felt was appropriate (assuming some more mature decisions).
I do understand the argument about preferring your kids to be in a safe place rather than behind the bus stop, but I also have my own principals, and discussing these with my dc let them know what my own stance was - and what I felt comfortable / uncomfortable about. So I was clear that I would not feel comfortable if my dc brought home a series of one-night-stands who I might meet fleetingly over breakfast, and I hope they know that I will lovingly accept anyone with whom they have a significant relationship.
NB to Mumsnet If this piece was prompted by a journalist, I do not want my response to be quoted in their article.