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Chicago Mayor Rahm Emanuel has ticked off the flocks by criticizing Chick-fil-A.

Days after the big city boss blasted the chicken chain over its president's stance on same-sex marriage, an influential Baptist minister and Cardinal Francis George of the Archdiocese of Chicago struck back. The religious leaders, who support the traditional view of marriage, were incensed at Emanuel's claim that "Chick-fil-A's values are not Chicago's values."

"Do not disrespect us...We, too, are Chicago," the Rev. Charles Lyons of the Armitage Baptist Church thundered from the pulpit Sunday.

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Cardinal Francis George also criticized Emanuel's stance, asking in the Catholic Chicago Blog if everyone who did not agree with Emanuel faced a similar fate.

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"Must those whose personal values do not conform to those of the government of the day move from the city," George wondered. "Is the City Council going to set up a 'Council Committee on Un-Chicagoan Activities' and call those of us who are suspect to appear before it?"

The controversy began when a Chicago Alderman Proco Joe Moreno said he would block the restaurant from opening a location in his ward, citing recent comments by Chick-fil-A President Dan Cathy. When asked about the company's values, Cathy was quoted saying he was "guilty as charged" for being "supportive of the family -- the biblical definition of the family unit."

Cathy also said on a radio program: “I think we are inviting God’s judgment on our nation when we shake our fist at Him and say ‘we know better than you as to what constitutes a marriage,’ and I pray God’s mercy on our generation that has such a prideful, arrogant attitude to think that we have the audacity to define what marriage is about.”

As officials in other cities, including Boston, San Francisco and New York, blasted Chick-fil-A over Cathy's beliefs, the company issued a new statement over the weekend.

"The Chick-fil-A culture and service tradition in our restaurants is to treat every person with honor, dignity and respect -- regardless of their belief, race, creed, sexual orientation or gender," the statement read. "We will continue this tradition in the over 1,600 restaurants run by independent owner/operators. Going forward, our intent is to leave the policy debate over same-sex marriage to the government and political arena."

But Lyons had a warning for anyone who tries to impose their values on his congregation.

"If the thought police come to Armitage Baptist Church, we will meet them at the door respectfully, unflinchingly, willing to die on this hill, holding a copy of the Sacred Scriptures in one hand and a copy of the U.S. Constitution in the other," Lyons said in the sermon.

Legal experts note that politicians, preachers and anybody else are entitled to their opinions on same sex marriage, which polls show the country is evenly split on. But they told FoxNews.com that it is disturbing that elected officials would threaten to use their power to block a company from doing business in their community because of a difference of opinion with people who work for the company.