Do traditional-minded Christians (i.e. fundamentalists, certain evangelicals) have more in common than not with Islamic values?

I am interested in hearing both from people who would consider themselves traditionalist Christians and those who would not!

On a recent trip to a more liberal Islamic country, I noticed that a lot of their views on topics like women’s place in society and the family; religious practice in governmental, educational, and public life; marriage and child-rearing were similar to what some fundamental Christians have been pushing for in the US. Both groups of people believe in strong nuclear families with the husband taking on the provider and natural leader role, while the wife takes on a more nurturing role focusing on the children and household management. They believe religion should be taught in schools and considered when making government polices and laws. They believe in the sanctity of marriage as between a man and woman and heavily frown upon premarital relations and unmarried women.

To caveat this, I do know there are of course differences in fundamental Christianity and fundamental Islam. But it seems less clear with more moderate/liberal Islamic countries like Morocco (the one that prompted this post), Turkey, Tunisia, Algeria, etc.