1. An immoral society affects us very much, no matter how much we try to shield ourselves.
2. This type of marriage will cause a breakdown of the family unit. Children won’t be growing up with a father and mother figure. It also affects modern orthodox (YCT types etc) who now want to include this type of lifestyle as normal, although the Torah is clearly against it.
Without getting too complicated, to live in a society that allows such a thing will impact our lives and lower the values in goyishe society as well.