Can you help me figure out what are the Culturally Christian things that one should avoid doing/saying?
Anon, it's not that simple. That's like a fish asking what aspect of water it should avoid.
I can also only speak from a white American perspective, as someone who was raised Christian and for a time, was Christian.
I don't avoid Christian things. They are part of American culture. I don't avoid Christmas with my family, for example.
However, as I'm now an atheist, I personally don't believe in a God, or Gods, or anything spiritual. But the culture I live in and the culture I was raised in is still steeped in Christianity.
And the influence of Christianity on me is something I've had to unlearn: virginity isn't special, sexuality isn't bad, sex before marriage isn't bad, things like that. There is no omnipotent force out there punishing you for "misdeeds".
I have worked to undo having a black and white view of morality; I don't think there's ever One True right or wrong reaction to a situation. I try to think critically when people discuss concepts like forgiveness because it's often from a Christian point of view.
I do not say "Merry Christmas" to strangers during holiday season; I don't assume everyone around me is Christian. I make an effort to be aware of other holy days throughout the year.
I learn about other religions from the perspective of people in that religion - I've learned so much about Judaism, for example, from Jewish folks here on tumblr.
Basically... you can't AVOID Christianity in America... but you can learn to see its influence, where before it was invisible to you. Question things you hear, and learn from others, because often stuff that is culturally Christian is so transparent from the inside you have absolutely no idea it's affecting you.