Muslim parents may feel they have more affinity with the Roman Catholic Church than "beer-swilling Celtic supporters at Parkhead", Chris Mason, Glasgow's Liberal Democrat leader, told councillors on Tuesday.
Dr Mason questioned the legality of moves to introduce a religious hurdle at overcrowded schools by requiring parents to prove a religious attachment to the Church. The policy was narrowly carried at an earlier meeting of the controlling Labour group by 26 to 24.
Glasgow will also insist parents make a placing request if they want to move between non-denominational and denominational schools within a catchment area. It believes a verdict in the Court of Session relating to a recent Dundee dispute justifies its stance.
But Dr Mason predicted that angry Muslim or Hindu parents might sue. "Does this city council want to be seen arguing in the Court of Session in favour of religious differentiation? This policy takes a risk with Glasgow's reputation in the interests of two schools, Holyrood and St Andrew's," he said.
Both are popular secondaries and attract large numbers of pupils from non-associated primaries.
Dr Mason later retracted his comments about Celtic supporters - "they're not all bad types" - but argued that Catholic schools were "not so fragile that they need this kind of protection". It was not in the interests of the city or education.
However, Peter Mullen, the Church's representative on the education committee, who is a former headteacher of Holyrood, said it was an "absurdity" that he had twice been to court to defend the existing policy of excluding Catholics because of an influx of non-Catholic pupils. "If we are going to have Catholic schools, surely to God, it is reasonable to have Catholics going to them. What is the raison d'etre of Catholic schools if it is not to provide a Catholic education for Catholic children who want it?" Malcolm Green, the education convener, said it was it "not unreasonable" to give preference on denominational grounds. Glasgow parents currently make more than 4,000 placing requests a year.
Meanwhile, East Renfrewshire has urged ministers to allow councils to set strict admission limits on popular schools which appeal committees or sheriffs would be unable to challenge.
The Scottish Office could act as a monitor to safeguard parent interests, the council says.