analytically, im not sure how one can grow up without faith and be socially conservative, the objective morals that faith provides creates socially conservative values in people. so in my mind people should bare minimum be spiritual to be conservative.
ask an atheist conservative why they think pornography is wrong, or why marriage should be between a man and a woman, or why we shouldnt teach LGBT in public schools.
their answer will either be libertarianesque or "thats just the way things are"
when they correct answer is, Pornography defiles the act of sex, which was created for a man and woman to use for enjoyment and procreation for loving couples not promote promiscuity or sexual violence. marriage is between a man and a woman bc God created Man in His image, then bore woman from his rib. marriage is the Union that brings the two back together. we shouldnt teach LGBT in public schools for one bc well christians pay taxes too and how awful is it the state gets to undermine parental authority, and two bc it teaches children to that its okay to live outside the way God created us to live.
so to answer your question, no athiests cannot be socially conservative. they are just faithless, self centered people. bc in 50 years from now, when people are trying to upload their consciousness into some kind of dystopian genderless AI server or androids, they will be saying that there is 87 genders actually, we cant be genderless, bc thats just the way things are, being socially conservative isnt about maintaining the status quo, its so much more than that, its about preserving things that made western civilization dominate the planet and living how God wants us too.