Gay Marriage and Abortion. I'm going to try not to provoke anyone. I just think it's a shame that liberals don't understand at all why conservatives feel so strongly about these issues.
Advocates of gay marriage will say "Marriage is just a legal arrangement between adults." That's exactly what religious conservatives fear it will become. To them it is more. It is the foundation of society. They are often suspicious of government, partly because governments come and go, so the civilizations which endure through all of the revolutions must be based on something else, some other organizing principle. They believe that organizing principle is family. Clan, tribe, kinship group... They believe blood ties, not legal arrangements, hold the world together. People who live atomistic lives in big cities and who are used to selecting and dissolving social groups, really live in a different kind of society altogether than rural people, who don't choose their relatives (or even their neighbors), but inevitably rely upon them. If more urban Americans understood what "family" means to people living less modern lives, we might have less trouble relating to Arabs and South Americans and South Asians as well.
Anyway, conservatives don't think that governments get to define marriage, and thus family, because conservatives think family is more fundamental than government.
People who are strongly pro-choice seem to think that anti-abortion activists just like oppressing women, that they're all men who'd like to see all women barefoot and pregnant... But actually the anti-abortion activists I know (through my mother -- Hi, Mom) are mostly female. They don't hate women. They don't hate sex, either, even if they do wish more people would get married first. They dedicate a lot of money and time to women's charities, because charity is an important part of their religion, and Mary Magdalene is one of its saints. No, this isn't about misogyny or puritanism. The problem is how to define a "person". It's a hard problem. In the past, we've excluded various races, those of several religions, my gender, people with certain disabilities, infants and young children. It's only going to get harder, as we start tinkering with the definition of "human" through genetic engineering, and eventually maybe even artificial intelligence or recorded personalities. (We still haven't worked out what sort of consideration we owe to creatures who are certainly not human -- are standards of animal cruelty different for mammals than for fish?)
Anti-abortion activists want to be generous in their definition of humanity. Some of them may even have seen (as I have, in a neonatal intensive care unit) infants born two months too early, almost small enough to hold in your hand, weighing in at a pound, like a tub of butter, with little cigarette-arms and tiny little finger nails and expressive faces. For now, those are about the youngest we can keep alive outside the womb, but I don't expect that to be true for very long. And anyway newborns are still utterly dependent upon their mothers, even meant to go on getting their nutrition from her body. So what's so special about birth? If not there, where do you draw the line? Are you really comfortable drawing it at all? And can you really blame anyone for wanting to draw it as inclusively as possible?
There's one more aspect to both of these issues which is worth mentioning briefly, and that's the role the courts have played in changing our national policy. The problem with court decisions on hotly debated issues is that they bypass the democratic process. Instead of votes among our elected representatives, we get a fiat. This inflames rather than settles the debate. It also requires some rather strained reasoning to argue that a constitution which mentions neither pregnancy nor marriage actually ties the hands of the state(s) on these matters. Debate and voting would be better approaches, slower, but more honest and with a more stable outcome. You can disapprove of the abbrogation of power by the jucial branch even if you support the causes these decisions favor.