Would it be acceptable for a Christian to celebrate birthdays?

If pagan ceremonies, customs, god names, etc. are really mixed in with ceremonies, customs, etc. that we use today, they are not merely unacceptable - - - they are detestable to God. We must completely get away from these unclean things and not even "touch" them! "Therefore come out from them and be separate, says the Lord. Touch no unclean thing, and I will receive you." - 2 Cor. 6:17.

Notice how exclusive the worship of God must be: "Be careful to do everything I have said to you. Do not invoke the names of other gods; do not let them be heard on your lips." - Exodus 23:13, NIVSB.

So again, if a holiday or custom (such as a Birthday) is being deliberately participated in by a Christian, it must have absolutely no known pagan religion associations.