Even people regarded as "unchurched" had warmed to the basic Christian view that marriage and the family are to be supported and defended, he said.
The Cardinal again attacked "homosexual unions" as means of raising children and argued it was "in no way discriminatory" to promote marriage as the foundation of family life. The best deterrent for teenage pregnancies was also "education in chastity", he said.
He added: "In recent weeks some very interesting things have happened in the sociology of the new Scotland. A kind of instinctive sense of morality has emerged which gives me grounds of hope that Christian values are still strong among our fellow Scots.
"In defence of the marriage-based family, Christians who are, doctrinally-speaking, poles apart, have come together in a way that no frmal ecumenical initiative could have achieved."
The Cardinal continued: "Even elements of popular culture, when challenged to side with a kind of values-free political correctness or traditional morality, have opted for the latter. That should encourage all of us who are concerned about the foundations of Catholic education."
Emphasising the centrality of Catholic schools to the Church, the Cardinal acknowledged that many other countries did not enjoy such well-organised and supported separate school systems. Five of the 11 new secondaries in Glasgow would be Catholic schools.
But updating teachers on moral issues required "urgent attention".
The Cardinal asked: "Who supports the teacher of modern studies by providing up-to-date findings on issues like population growth? Who helped the biology teacher with the Church's insights into bioethics? Who keeps the religious education teacher updated on the latest encyclicals, the findings of synods or the latest pastoral insights?"