I would not allow someone else to BF my child. I think I have a really strong reaction against this idea because I had to fight so hard to continue to BF DS, and had to start supplementing with formula, but have continued to BF and still am now that DS is 16 months. I really felt that my body let DS and myself down, and I felt very jealous of women who had plenty of milk, and inadequate compared to them. So I think I very jealously guard my BF relationship with DS. All the milk I have is for him, even though it was not enough, but we still have made it work for us. I'm not sure I'm expressing myself very well (no pun intended!) but for me it's a relationship I had to fight so hard for and I wouldn't want anyone else stepping into that.
I can absolutely understand that. If I hadn't successfully BF'd DD2 I would feel very much the same, as I still feel quite sad about missing out on being able to BF DD1. It's a very valid opinion, you're not alone at all

As for me BFing other people's kids... I have to say as long as it was comfortable for me (ie the baby didn't bite or hurt me lol) I'd be okay with it and wouldn't feel that bond that we feel with our own babies, but for some reason I'd still be weird with someone else feeding my baby - I can't guarantee that they're not enjoying it, kwim?? If I could ascertain I had a very plentiful supply for both my bub and another, I'd be more than happy to express for someone else's baby, but I found expressing extremely difficult both times, even when engorged with DD2 and having 'lots' of milk to spare, so if I were to step in for someone it'd probably have to be on the boob rather than EBM.

I have to say I'd be a lot happier about someone breastfeeding my child if I were (god forbid) dead or severely incapacitated. If it were an emergency babysitting situation or something like that, I'd be less comfortable with it, but that's I think those jealous mummy feelings kicking in. If I were, say, to die in a car accident and had a BFing baby at home, I wouldn't be around to see them form that bond with anyone else so I'd be happy for another woman to BF, itms...
Good question, awesome thread. Great to see everyone's individual stance and conditions and motivations put out there