Rt Revd Dr Ian McNie said tolerance was "a two-way street" and that the Church had "the right to expect the same level and proportion of tolerance afforded to us that other groups expect afforded to them".
He was speaking following his formal election and installation and said that whilst maintaining his opposition to same sex marriage he recognised some in society were in favour.
"As a church we must defend the right of society to freely express their opinions," he said.
The clergyman, 64, added: "By definition tolerance accepts there are different opinions and that we should agree to disagree in an agreeable manner, not the definition that is currently postulated, that tolerance is the acceptance of different opinions and that all opinions are equally correct and should be endorsed as correct.
"This leads to a position where Christians are required to promote ideas and deliver services that are contrary to their beliefs. True tolerance can only flourish in an atmosphere of mutual respect in disagreement.
"And why mutual respect – because God's Word affirms the unique dignity of every individual, each of us being created by God with value, purpose and destiny, and that equality should not be seen simply as the result of governmental legislation but the result of birth as each person is individually created in the image of God."