I recently had a relationship conflict with someone who I have religious differences with... He is Christian and I do not believe in God.

Although I do not believe in God, I do believe in religion. I want my kids to go to church (probably whatever religion my partner is) because I feel it would be a cultural disservice to them to not be exposed to that. I will not try to convice someone to not believe and do not wish to be convinced either. That is not a religious or faith issue to me; it is a personal respect issue. I celebrate the major holidays (as it represents family time and my family believes in God) and want my children to do the same. I would be more than willing to be married in a church, go to church with my partner, and fully support their religious faith.
I was brought up in church and did personal investigation into eastern and western religions and came to my own conclusions. I fully respect someone who has come to a different conclusion. My lack of faith has zero bearing on my life and the choices I make. I do understand that faith can have a high bearing on other people's choices and would support a partner who holds that to a high importance.

So my question here from a Christian POV: Would this matter? Or is the fact that I simply don't believe in God trump these things?

Yes, to a real christian, not the one who just goes sometimes to church, being yoked with a unbeleiver is very much warned against, For example, the celebration of "holidays" has little to do with the way the US celebrates them, since at home the real meanings of these holidays need to be taught, and christianity is not something you just do on Sunday, but something the entire family does, it is part of your life every day, prayers at every meal, the charity work and talking and teaching the child about your faith at home.

A person of high faith and importance of the faith would cause serious issues in all aspects of life.