They're all thrown in the same basket together because they all prove that sex between a husband and wife for the purposes of procreation only isn't a human's natural inclination. Like anyone who's trying to con people, they'll lie to sell their worldview so that people do what they want.
We humans are complex animals and we have complex needs. Telling people to do it at certain, limited times in certain, limited situations is about the same as telling people not to talk to others or not to eat every day. We're not machines and we're not robots - we have needs that can't be easily quantified or valued but are no less real that other needs that keep us alive. Sex and relationships seem frivolous in a post-industrial culture next to money and productivity, but they're the very reasons we have to stay alive.
Contraception is a great invention; in a society where raising a child is expensive, women should have the choice of conceiving or not. The planet already has enough people on it and if someone doesn't want to raise a child, then they shouldn't have to. That seems fair to both adults and potential children.
Divorce is good - it gets people out of relationships that are no longer working for them. Unlike what Disney and the Religious Right would have you believe, people don't always live happily ever after. People assume when they marry that it's going to last forever, but life happens and there's no reason to spend the tail end of one's existence with someone who one can't stand.
Cohabitation is one of the better ways to combat loneliness. People are social animals who need to live with others, eat with others, talk with others to even have a sense of who they are and that they belong on this planet. Even if unmarried people don't have a piece of paper from the state, they have the same needs. I've lived alone and I've lived with others (parents and siblings, then roommates, now my partner), and I prefer living with others no matter what relationship I have with them.
And same-sex unions... I can't imagine a reason why people shouldn't be allowed to love the people they love. Love is good! Genitalia shouldn't matter when it comes to approval of other people's relationships. (I know, I'm preaching to the choir here.)
All these things are related because it takes a certain authoritarian mentality to believe that people can just follow orders and be productive little machines with no needs of their own. It's a leftover from our Victorian legacy where servants weren't supposed to even be noticed - now the Religious Right is trying to get the masses to shut up and accept their lot in life without complaining that they don't have a reason to live.
Peasants, meaning is for real humans! You just make stuff for us and serve us and keep quiet!