Does Krishna consciousness forbid marriage and sex?
No, marriage is all right. But sex outside of marriage binds one to this material world and so is counterproductive from the spiritual point of view. The point is that sex for other purposes than producing God conscious children makes us more materialistic and slows our spiritual progress.
Simply put, if you get married and engage in sex for fun instead of producing a child, that act will make you more materialistic. It will cause you to identify yourself more with your body and more as an independent enjoyer rather than servant of God, the supreme enjoyer.
The pure consciousness of the soul is to please God. So sex for producing children that are taught God consciousness is a spiritual experience, otherwise sex is material. As mentioned above, sex for producing children is OK. Sex for recreation is an impediment to spiritual progress.