I haven't been in this situation yet but I'm sure I will be.

I think my stance would be this. If I liked DD's friend and she wanted to invite her for a playmate, then I'd keep inviting her. Kids don't choose their parents and if for some unknown reason, the parents did not like me or my child then that's their problem.

As for the party, extremely tricky, but again, if I liked DD's friend then I'd hope we could move past it. Maybe the parents over-ruled them. At the end of the day there's a myriad of possibilities but if the children want to be friends and if I think the other child is a 'good kid' then I'd hope I could prioritise that.

Whole different kettle of fish if I didn't want DD to be friends with a particular kid. There's a couple of girls at DD's kindy who seem (admittedly from the very snatched interaction I've had with them so far) to be a bit mean. I won't be encouraging that friendship even though their mums seems absolutely lovely and people I'd get on well with. On the other side, the kids who DD plays with the most seem kind and a lot of fun. Unfortunately, their mums seem boring and one-dimensional. Clearly, I'm going to have to suck it up.