Economics and ethics
Few things rile up people more than their views on economics and ethics.
Economics in the sense that money spent on one thing means less money (or no money) spent on another. Or, even, when money takes the form of time (because time is money)—how that time is spent.
Ethics, in the sense that our decisions and actions are binary. In that there’s a ‘right way’ and a ‘wrong way’ and we only get one choice we can take as a community.
On the other hand, if we somehow discovered that a colony of people on some distant planet believed in a completely different set of beliefs than we did, most of us would have no problem. Similarly, if some alternate-universe existed that took an entirely different stance than the one we voted for, we'd care very little about it, because even if it was a binary choice, we (as in our culture and community and our sense of how things are) wouldn't be effected at all.
The trick, I think, when it comes to living with people who share dissimilar beliefs, who simply want to live their lives on their terms, not ours, is to consider whether we'd care about those choices if they were made so far away we wouldn't notice.
And then to acknowledge all the times and places when those decisions--for better or worse--really won't effect us at all.