So what has changed? We have not moved and my daughter still sees most of the children in school who were at that party. Without any obvious fallings-out, those who are not like her no longer receive invitations.
Similarly, my six-year-old's nursery-age parties used to feature a mixed bunch, but once in school she instituted her own strict admission policy - no boys and no non-white girls.
When asked, both girls still count Asian and black classmates as friends, but stop short of wanting them at their parties.
This apparent incipient prejudice alarms me: am I not setting a good example? My closest friends are generally white northern migrants to London with working-class backgrounds - just like me. In my defence, I have never had the opportunities my children have to mix, growing up in predominantly white schools, and working in a mainly white industry, although my wider circle includes Asian and black people.
Are my children just naturally finding their own reflections and imitating my discrimination in whom I chose as close friends? Are they just following a pattern set by generations of pupils in their school? Or given the timings of the shift, is something happening in school which is not conducive to keeping inter-race friendships?
In nursery, the girls were introduced to different religions in the guise of festivals. But Divali, Eid, Christmas, Passover et al were often excuses for a party or a sticky card-making session. They were like birthdays, celebrated by some on one day and by others on another.
But almost as soon as they moved over to the "big school" they were taught what these festivals represent. Children, who are still trying to establish their own identity, are made to look at their classmates in terms of their religion - which in most cases also equates to skin colour. Now not only do other children look different, their lives are presented as different, in ways that must seem insurmountable.
What does a four or five-year-old imagine goes on inside a mosque, synagogue, temple or church if they have never stepped inside any place of worship, let alone only one sort?
How can we expect our children to be friends with someone who spends Friday or Sunday involved in odd activities? At that age what you do not understand can be disturbing - who wants a friend who disturbs you?
When discussing the elder daughter's seventh birthday party, to be held on a Friday, I suggested a friend who was regularly mentioned. But she was not keen. When pressed, she became shifty.
Yes, they were still friends. No, they had not fallen out. She eventually confessed: "I won't be able to have sausages, and she probably would have to be at mosque anyway."
The piecemeal information she had received had put her Muslim friend in another realm. The problems of vegetarian friends and sausages had never occurred to her, but thanks to formal lessons on Islamic dietary rules and how they should be respected, they had assumed a disproportionate significance. Yasmine now was no longer just Yasmine, but Yasmine-who-could-not-eat-pork.
Are we expecting too much of young children to ask them to digest religious beliefs and practices, and then not look differently on their classmates?
These are youngsters who are requested in maths and science lessons to sort objects into groups and asked "Which is the odd one out?" They want to be in the right group and if religious observances are so important, and they must be because their teacher said so, then no wonder they separate.
I want my children to grow up respecting and valuing others' beliefs but I cannot help wondering if we would not be better off waiting until they have had time to appreciate individual children, before we start loading them down with the differences. There are already too many other negative influences out there which affect how children make friends. Could schools not help by allowing their pupils to forge proper friendships first?
Religion will then be just one aspect of that friend, not their all.
Alison Shepherd is chair of governors at a north-east London primary