Courting is not marriage. If someone you are courting suggests that, you need to RUN in the other direction -- as far and fast as you can.
If someone is willing to cut ties to friend because they marry they are not a real friend.
I don't think men and women should be alone in a closed setting (car, home) even if both are single.
We should probably define our terms. When I say "close friends" I mean that good friend from childhood that you've known forever. "She's a sister to me!" kind of thing. A regular friend would be someone that you hang out with when you're with a group of friends. A close friend would be "Hey, lets go grab some lunch and catch up". A regular friend would be "Hey, lets grab some buds and go snowboarding!". I don't know if that makes any sense. In most of my friendships the "close friend" is someone you can hang out alone with and talk about personal matters. A "regular friend" is part of the whole crew of friends.
I guess "cutting ties" was kinda harsh. I meant that you should spend less time with that person, and never alone but in the company of your spouse.