Which Christian men? The Orthodox?
All denominations from multiple countries at different times in history. Anglican Puritans in the 1700's, French Huguenots in the 1800's, Greek Orthodox fleeing Egypts Nasser in the 1950's are a few examples. There has been a consistent pattern of Europeans abandoning their home country and relocating to the frontier, and its these people who built countries like the USA, Canada, Australia and New Zealand. Many also moved to countries like South Africa, Argentina and Brazil too. What has been achieved by these people is nothing short of amazing and it was achieved by people who decided to pick up and move.
When it reaches a point where the majority of the people you are trying to coexist with no longer share your values and you are being treated as a pariah because of the values you have? You have no obligation to these people at the expense of your own family or future, and you really do need to be asking yourself if you are being complicit in propping up a system which is ultimately hostile towards your core values.
You have three options IMO.
1 - You can stay, try and tolerate it and pray for a cultural shift
2 - You can try form a parallel society so that you exist alongside it, but you need to sever your reliance on that society (Mennonites, The Amish, Mormons to a lesser degree)
3 - You move to a place where your fundamental, core values are shared and you integrate accordingly.