When you take the time to explain the origin of every word of your language, any cultural influence on your food preferences, clothing, choice of furniture, music appreciation, etc. rather than just accept that you are a product of your environment, experience, as well as being uniquely your own person, then you can require that of Christianity. In other words, it would be ridiculous for you to have to acknowledge such every time you speak about anything related to yourself.
I don't think the vast majority of Christians have ever denied the cultural influences that have been incorporated into Christian language, customs, and rituals. I know that as a Chrisitian teacher, I actively teach such.
But to have to acknowledge these every time the subject comes up would be ridiculous. As would it be ridiculous for me to explain that the architecture of my house has a Mexican/Spanish influence every time I refer to my house which is not Mexican/Spanish but was morphed into an architectural style that has become its own thing common to this area.
The things which we enjoy, appreciate, are comfortable with can encompass a great deal of the world's culture just as many of the customs/traditions of the pagan world of the Roman Empire predated the Roman Empire. There simply isn't time to footnote everything each time we talk about it.
That you share similarities with other people and demonstrate traits that result from your experience and heritage does not change the fact that you are your own person. That Christianity shares similarities or shows influence of past cultures does not change the fact that Christianity is its own thing.