The Home Secretary has told a Westminster audience that the fundamental principle of equality must not be undermined.
Reid, a Roman Catholic, is considered one of the only members of the Cabinet who could mount a serious challenge to Gordon Brown in the contest for Labour party leader, due to take place after Tony Blair leaves office later this year.
Speaking at a lunch in central London, Mr Reid chose to deal with the ongoing controversy about a possible opt-out from the Sexual Orientation Regulations for Roman Catholic adoption agencies, allowing them to deny gay or lesbian couples the right to be considered as potential parents.
“If you bring in a law which says all people will be treated equally, then all people will be treated equally, he said, according to the Daily Mail.
“I don’t believe you, in this country, have the right to overrule some of the fundamental values on which the country is based because you have a conscientious objection. That’s my view.”
Mr Reid also told the audience that ways should be found to help people of conscience abie by the law, but that fundamental values have to be accepted by all.
The Sexual Orientation Regulations are due to come into force in April.
They protect gay, lesbian and bisexual people from discrimination when accessing goods and services, which includes adoption agencies.
His comments come at the end of a day when the press have revealed that MPs and Labour Cabinet ministers have persuaded the Prime Minister to abandon plans to grant an opt-out to Catholic adoption agencies.
Senior Roman Catholic figures had threatened to close adoption agencies rather than allow gay or lesbian couples to be considered, despite the fact that single gay and lesbian people have been approved as parents by Catholic agencies in the past.
Mr Blair issued a statement this afternoon saying he is still hopeful he can work out a solution that will balance the demands of the Catholic hierarchy with the rights of gay and lesbians.