To accept that things can't be reconciled because people are different, allow people the individual right to be different, and protect everyones equal right to do their own thing without fear of loss of life, liberty, or property caused by others without just cause (eg: the defense of life, liberty, and property from someone else who initiated an unwelcome infrindgement)
That is the basis of liberty, and the role of government is simply to protect liberty. Nothing more.
There is nothing wrong with not finding middle ground because it's ok to have differing views. Governments role is to be neutral and keep the peace so that each is free to embody his/her own view, not to take a side and butcher both views with a comprimise and try to force everyone to be the same.
eg: if you don't like gays, hate guns, and are concerned about the environment, then you have a right to not be forced to be gay, a right to not buy a gun, and a right to drive a Prius without anyone being able to stop you. However, COMPRIMISE comes in the form that you likewise have no right to prohibit, via by law or other means, someone else from being gay, owning a gun, or driving a Hummer. You don't have to agree with it, you just have to sit there and accept it.
Government is intended to keep the peace and allow everyone to be different, the upholding of individual liberty, not what it has become, a vehicle for 51% of the people to use anonymous force to enact their views and take away the rights of the other 49%.