In Noah Webster's 1828 dictionary, there is no meaning of the word culture as it can be used at times today. The 1828 meaning basically defines it as any labor for improvement or growth. When did this word change its meaning? The reason I was thinking about this is because some people who call themselves Christian refer to the Bible's "culture" at the time. Someone has told me that in the culture at the time of the Bible women couldn't be a pastor. I have heard others refer to a  "Southern" culture or a "Northern" culture. In these times when diversity and tolerance is stressed in and outside of the "church", this word is used (or misused) frequently. Another phrase used is "culturally relevant". It may be culturally relevant at one time but not another. Of course it is comforting to know that the Bible transcends all so-called "cultures"!

The word, culture, is not in the Bible. In fact, it originally meant cultivated and referred to a piece of tilled land. Later, it was used of a person in reference to the cultivation of their mind and manners. Only In the late 19th century, does it seem to have taken on the idea of the ways of a civilization. However, that does not mean that the Bible has no concept of culture as we understand it. Although the word culture is not used, we find other words that refer to the different practices of societies at different times. For instance, the Bible refers to the manners, customs, and ways of different peoples and times. This is, in effect, referring to their culture. Ruth 4:7Now this was the manner in former time in Israel concerning redeeming and concerning changing, for to confirm all things; a man plucked off his shoe, and gave it to his neighbour: and this was a testimony in Israel.
See All... refers to a ancient custom: "Now this was the manner in former time in Israel concerning redeeming and concerning changing, for to confirm all things; a man plucked off his shoe, and gave it to his neighbour: and this was a testimony in Israel." Jeremiah refers to sealing the evidence of his property purchase "according to the law and custom" (Jeremiah 32:11So I took the evidence of the purchase, both that which was sealed according to the law and custom, and that which was open:
See All...). Paul refers to "the manner of the Romans" in his own defense in Acts 25:16To whom I answered, It is not the manner of the Romans to deliver any man to die, before that he which is accused have the accusers face to face, and have licence to answer for himself concerning the crime laid against him.
See All.... All of these and more are the elements of the culture.

In the examples in the preceeding paragraph, the ways of the land are benign. They are not necessarily right or wrong in an absolute sense. However, the Bible often uses the concept we would now call culture as a negative quality. The Israelites are warned against following after "the doings of the land of Egypt" or "the doings of the land of Canaan" (Leviticus 18:3After the doings of the land of Egypt, wherein ye dwelt, shall ye not do: and after the doings of the land of Canaan, whither I bring you, shall ye not do: neither shall ye walk in their ordinances.
See All...). They are not to walk in the "manners of the nation, which I cast out before you" (Leviticus 20:3And I will set my face against that man, and will cut him off from among his people; because he hath given of his seed unto Molech, to defile my sanctuary, and to profane my holy name.
See All...). The Lord warned in Jeremiah 10:2Thus saith the LORD, Learn not the way of the heathen, and be not dismayed at the signs of heaven; for the heathen are dismayed at them.
See All..., "Learn not the way of the heathen." The corruption of Jerusalem is pictured by her doting on pictures of men who were attired "after the manner of the Babylonians of Chaldea" (Ezekiel 23:15Girded with girdles upon their loins, exceeding in dyed attire upon their heads, all of them princes to look to, after the manner of the Babylonians of Chaldea, the land of their nativity:
See All...).

From these passages we learn several things:

1. There are manners, ways, and customs that are connected with certain societies and certain times. That is, there is such a thing as culture as we now use the word.
2. Some manners and customs are neutral in their spiritual significance. One way is not spiritually good and all other ways spiritually bad. They are simply the different customs and manners by which men have learned to operate within their own societies. NOTE: These differences are not good and bad. Therefore, it is not the calling of Christianity to change these ways when people in these societies are won to Christ. They can be good Christians while continuing in the cultural practices to which they are accustomed.
3. Some manners and customs are spiritually wrong. In these cases, true believers in any culture should be taught to go against their culture in obedience to God's word. For example, tribal converts should be taught to cover their bodies. Head-hunters should be taught to change their ways. It is a danger to agree with the liberals that all cultural differences are neutral. They are not. Some practices are wicked and should be altered in the lives of believers--even to the point of opposing their own culture. This is part of being a "peculiar people" (Titus 2:14Who gave himself for us, that he might redeem us from all iniquity, and purify unto himself a peculiar people, zealous of good works.
   See All...).

You have wisely referred to the false teaching of many who use "culture" to change the meaning of scripture. For instance, women pastors may not have been allowed in their culture, but it would be fine in ours. This goes blatantly against the extensive teaching on this subject in scripture. It goes against the strong biblical arguments used in places like 1 Timothy 2:12-14 [12] But I suffer not a woman to teach, nor to usurp authority over the man, but to be in silence. [13] For Adam was first formed, then Eve. [14] And Adam was not deceived, but the woman being deceived was in the transgression.
See All... and 1 Corinthians 11:3But I would have you know, that the head of every man is Christ; and the head of the woman is the man; and the head of Christ is God.
See All..., 8-9. The idea of being "culturally relevent" is often an excuse for denying God's holy word. We should treat it as such.

Are there cultural differences between societies and across time? Yes. And, they have to be dealt with. If they are neutral, then converts can certainly continue in their respective customs and practices. However, when and where they cross God's line of right and wrong, they need to be changed. That is part of being a new creature in Christ.