What part did the culture of the Paul's day play in the regulation(s) of the new born church in regards to women serving in the church and has it changed?
Yes, the culture has certainly changed in many ways since then.
The question is (as someone has alluded) are we given any latitude to change along with it in regards to women's service?
Paul uses phrases like "your women" but later uses "women" in a generic sense.
Personally I have a bottom line in my view of these scriptures: that the authority of the male leadership not be usurped.
I don't believe a woman should be a pastor. If she is single and feels led to the mission field, she could have a teaching ministry to women and children, or as a doctor, nurse, etc.
But, I don't believe the 1 Corinthinas passage disallows singing, praying, giving testimony or teaching other women and children but is in the context of teaching men and the appearance of usurping the ordained authority.
Also, a woman missionary or missionary wife or pastor's wife should be able to give a report or testimony to a mixed audience of men and women assuming the pastor and/or her husband are present in the church.
Then there are "offices" in which women participate .e.g. Sunday School superintendant, Mission board, financial board, librarian, etc.
Compromise? Maybe, but as long as the male
leadership and doctrine is not compromised IMO it is allowable. Maybe not the best decision but allowable.
Where would we be if all the women in all Bible believing churches kept the letter of the NT rules - absolute silence?
Corinthians 14:35 And if they will learn any thing, let them ask their husbands at home: for it is a shame for women to speak in the church.
Could any church find enough qualified men to fill these roles above?
No female Sunday School teachers, no singing, no praying out loud, no testimonies, no report(s) to the pastor and deacons (in the church), no children's church, etc...
What about pot luck dinners are women to prepare and bring the food to church and then eat in absolute silence? May it never be (in the words of Paul)!
Is absolute silence what Paul meant (I don't think so as there are other places he talks about women praying, prophecying in church)?
If it's not what he meant then because of church autonomy every local church must decide those parameters.
HankD