The basis for atheist conservative cooperation is liberty. Core conservative values include Free Markets, Security and Defence, Personal Liberty, Nationalism, and the Rule of Law. Personal Freedom includes freedom of religion or lack thereof. The same values protect the rights of atheists as they do the rights of the faithful. We all want the same thing. Freedom.
There is no reason for any conflict between atheism and conservative values, even those of social conservatives. The faithful believe that rights and freedoms come from God directly. There is no government or even a religious official that can revoke the rights of a Human Being. Freedom is divine.
The thinking atheist, ones who take the time to think about the nature of freedom, knows that rights and freedoms are inherent to Human life. There is no government or scientist that can revoke the rights of a Human Being. Freedom is Human.
The theological and philosophical debate as to the existence of God should not have any bearing on policy or politics at all. The true God would never revoke the free will and divine rights of humans. A non-existent God will never be able revoke the free will and divine rights of humans. Effectively the atheist conservative and the conservative believer have the same position on liberty whether God exists or not.
The left wing view is that rights come from government. They replace God with government and submit to the dictates of men with power. A right can't be over ruled by definition. Rights are not rights if they are subject to the approval of others. Rights supersede laws, opinions or policy. The idea that rights come from government is internally inconsistent like so many ideas on the left.
The conflict between many atheists and conservatives also comes from the left. Too many atheists enjoy a feeling of superiority that enables them to belittle and insult believers. The main target of this branch of atheism is social conservatism. This has been the case since Marx called religion the "opiate of the masses." Extreme socialist regimes have adopted atheism primarily to take power from religions and to encourage the same sort of intolerant superiority that pervades the left today. Left wing atheists are tools of the left. They mobilize one group against the other to further their socialist agenda.
Left wing atheists typically ignore those believers who think the job of government is to enforce the social moors that come from religion. Take the blind leftist support of totalitarian Islamists over freedom loving Jews in the middle east as a prime example. Atheists are free in Israel while they can be murdered or executed in most of the middle east. What other word than 'tool' can be used to describe a left wing atheist. A person turned against themselves for no better reason than their political faction is allied against people they locally dislike.
Left wing atheists have been marshaled into war with social conservatives for a long time. Now is no different. Religion is not the enemy. Overbearing government is the enemy of all humanity. Conservative atheists have a responsibility to turn other atheists back to liberty through solid reasoning. They also have the responsibility to defuse the tension created by the left towards all atheists. Believers are good, hard working, intelligent and freedom loving people. They deserve respect even while we might respectfully disagree on the remote yet fundamental aspects of nature.
A excellent lecture on Ayn Rands Theory of Rights by Objectavist Craig Biddle can be viewed below. He has a corresponding essay that goes deeper into the ideas here.
Ayn Rand was a great atheist and philosopher who discovered and put into language what many atheists already believe but are unable to express. Religion has had thousands of years to refine their arguments while the atheist awakening is still rather new. Not enough time has been spent by atheists on the questions of rights and morality resulting in many minds lost to socialism.