Can Atheists and Believers be friends?

No! Not at least if they both hold their respective positions with ardent passion and conviction. If the believer is a Sunday worshipper and never a religious sentiment ever trips from their lips - and from my experience  most believers seem to fall into that category - then yes, because the subject never arises and a friendship can very easily be had.

If both parties can agree tacitly not to bring up contentious issues a friendship of sorts is possible especially as atheism is not an ideology - as born out by the fact that an atheist can be a communist, socialist, fascist, liberal, neo liberal, pagan, conservative,neo conservative, etc etc -the word atheist only connotes an absence of belief in God, not what the atheist believes in and their philosophy of life.

If the atheist is kind of wishy washy in his atheism and is not philosophically passionate in any direction such a person could have a believer as a friend but if  he is a committed Objectivist then friendship with a believer is only possible if the latter is a Sunday worshiper and the subject of faith never comes up. The only exception would be a wishy washy objectivist for whom his philosophy is lightly held in which case compromising with the friend of faith would be no bid deal for him or her!

Speaking from my position such a friendship with a passionate person of faith would be untenable and here's why. Imagine if that friend believed in fairies at the end of his garden and every time you met he wanted to talk about them, give a lecture on them, how he communed with them, how they influenced his every step and then harrangued you about it,warned you that denying the existence of those fairies who so obviously and manifestly do exist is to run the risk of a fatal end that will actually go on for all eternity as the faries in question will abandon you to your fate and will cast you out into eternal darkness. How would that situation be conducive to anything other than conflict and rancour? Would the situation in any way be improved if said 'friend' informed you that he was doing all of this for your own good because he loved you?! Take it from there as Miss Rand would say.