If you can weaken or break a person's faith and get them to accept something like same sex marriage (After all, it's just two people who love each other...), or if you can weaken one church's stance on the sanctity of life (Hey, the Catholics are going to have to pay for their employees morning-after pills...), it's much easier to get society to accept things that are immoral and ultimately inhumane; things like euthanasia of the old, the "unfit", or those who require expensive treatments; the sexual exploitation of children; selective abortions for gender or physical traits, and then the elimination of those who "don't agree with our world view".
Those who fully accept what you quoted, and understand that the slippery-slope argument is valid, and are therefore willing to draw the line at the small things; are known as rigid, harsh, unbending, patriarchal, straight-laced, puritanical, hard-asses.