As the mother of boys with special needs that could involve behavioural issues, and now a foster carer of children with various difficulties, I would be disgusted that the nursery had given any details about them to other parents. I would be extremely angry that they had tried to suggest your DS for not playing with them. It is so, so, so hard for children with additional problems to make friends, and for the nursery to make it worse in this way is disgusting. Do you know their mother, OP? If so I would make it clear what has happened, so the parents can make a formal complaint against the nursery and also remove their children immediately.
However, if I was you I would also think twice about leaving your own children there also. If they can give sensitive (well any) information about other children to you, they can equally give information on your children to others. In your case I would honestly find somewhere else for your children.
Can I also mention that my children and now foster children were also never invited to any child's home to play because of their special needs. Never invited to parties either, throughout their whole school life. I cannot tell you how delighted my children/foster children would have been should any lovely mother like yourself invited to another child's home. Even though my children are now mid 20s, the legacy of their school life remains with them, and to this day they are always overly grateful and excited if anyone issues any invitation. Your invite could really make the children (and their parents) week/month/year. Please do if you possibly can.
The person at the nursery who you spoke to should be sacked immediately, and if this is standard practise then it should be shut down. It is beyond disgusting, and breaking every rule in the book. I cannot tell you how I angry I am even reading about this situation second hand. Horrible.