Praise be to God.
Actually, you misunderstood this verse:
”O you who believe! Take not the Jews and the Christians as Awliyaa’ (friends, protectors, helpers), they are but Awliyaa’ of each other. And if any amongst you takes them (as Awliyaa’), then surely, he is one of them. Verily, God guides not those people who are the Zaalimoon (polytheists and wrongdoers and unjust)”
In here it means that you can take a Christian or Jew or any kind of disbelievers as your best friend with the following conditions:
Your Christian or Jew friend should not be taken against Muslims
You only can take Christian or Jews as your friends who do not mock or make fun or insult any element of Islam.
You can take any kind of disbelievers as your friend as long as he or she is treating you with respect, and does not do anything that goes against Islam.
You can take any kind of disbeliever you want as long as this person does truly respect the ways, believe etc.. of Islam.
You can take any kind of disbelievers as long as they are truly not against you.
Also prophet Muhammad married a Christian woman name Marie and then she became a Muslim. So according to this, you can be friend with anyone you wish, either with an atheist or anybody you wish. And of course, when we read a Hadith, we need to try to understand it instead of misunderstand it.
And God knows the best.