If a holiday or custom is being deliberately participated in by a Christian, it must have absolutely no known pagan religion associations.
God has always demanded that our "sacrifice" to him, no matter how small, must be pure and untainted. The principal was laid down repeatedly in the O.T. E.g., "Do not sacrifice to the LORD [Jehovah] your God an ox or a sheep that has any defect or flaw in it, for that would be detestable to him." - Deut. 17:1, NIVSB, (Cf. Lev. 1:3,10; 3:1). Even in "grain offerings" when the grain was made into flour and baked before it was offered, there was to be absolutely no leaven or "yeast" in that offering. The leaven, then, was figurative of an impurity, comparable to a defect or flaw found in an impure animal sacrifice, and made such a flawed sacrifice detestable to God.
So, can we get away with a tiny bit of "leaven" in our "sacrifices" to God today? No more than we can get away with a tiny drop of cyanide in a glass of pure drinking water. Paul tells us of a saying that makes that very point:
"Have you never heard the saying, `A little leaven leavens all the dough'? The old leaven of corruption is working among you. Purge it out, and then you will be bread of a new baking. As Christians you are unleavened Passover bread .... So we who observe the festival must not use the old leaven, the leaven of corruption and wickedness, but only the unleavened bread which is sincerity and truth." Further explaining, Paul says: "you must have nothing to do with any so-called Christian who leads a loose life, or is grasping, or idolatrous.... You should not even eat with any such person." - 1 Cor. 5:6-8, 11, New English Bible.
No, God still tolerates absolutely no "leaven" mixed into the Christian "sacrifice" of true worship. "I the LORD do not change." - Malachi 3:6, NIVSB.
Note the example of the golden calf. It was made from the gold jewelry of the Israelites themselves. Obviously the Israelites were not allowed to keep that pagan image of the calf no matter how they "cleansed" it or "gave it a Godly purpose"! But surely they could recast that extremely valuable gold back into jewelry or even into utensils properly used in the worship of Jehovah!! But no, in spite of its great material value, it must never be used again by God's people in any form, for any purpose! - Deut. 9:21. What could be a more obvious demonstration of the exclusive devotion required by God and the lengths God's people must go to to ensure pure worship? We must not knowingly "purify" and "reuse" anything that has been made for paganistic false worship!
So, if pagan ceremonies, customs, god names, etc. are really mixed in with ceremonies, customs, etc. that we use to honor God and Christ, 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.
So again, if a holiday or custom is being deliberately participated in by a Christian, it must have absolutely no known pagan religion associations.