I don't have an issue with the 'mixing' at all and would stay out of this if I were the OP: what I am saying is that, on a practical level, I don't know that I would be comfortable putting myself in a position where I would have to have a conversation with a "Shannon Matthews' Mum" type of person where I tried to convince her that it was okay for me to keep my child away from hers because, well, you know..
Encouraging your child to form a relationship with someone that you are not going to allow as an equal friend (e.g. you will readily let your LO go to Targuin's for tea but will not allow your LO go to Shannon's despite her pleas) is also problematic in terms of managing the situation and in the message you are sending. It seems like you are advocating a 'charitable concession' instead of being plain and transparent about your concerns.
For me, these concerns would relate to my child being in the house or the child's family potentially having an issue with either my child or me and, well, knowing where I live. As we should know from MN, parents frequently take issue with one another over minor issues.. however, a bit of shunning at the school gates is one thing, being glassed in the face by an angry thug of a parent is another.
For me, this a genuine fear based on incidents that have occurred in real communities in which I really, really live. "Wide spectrum of society" does include violent thugs. If Mr Murderer's son down the road is a fine, upstanding young man - good for him! But I do not want to even enter the fringe of the circle of Mr. Murderer so, well, his son will have to look elsewhere. It's not a class thing as people seem to be making out, it's a fear of violence-and-chaos thing. Having grown up in a house like ILoveTiffany's, I have had glimpses of both but thankfully not of the kind that gets the entire family sent down for GBH etc. There is NO WAY I want my child to be put in a position where they are encountering people who are violent criminals. Irrespective of how fantastic the child is.
In the teenage years, it is different. We are talking about kids, so there is an expectation that the families will have to at least make chit-chat in the course of the children's friendship. Again, I don't want to have to make chit-cat with violent criminals or even enter their radar.
We live on an ex-council estate that is part-council, part-private and I have NO issue with my child forming friendships with any child because of their economic background. I draw a line at violent criminality. I don't want anything to do with it, I don't want to invite that trouble into my life.. I really don't equate wanting to avoid that with living in an Ivory Tower.