I have met the parents of someone I am dating four times. One of those was under strange circumstances and wasn't really a 'meet my parents' sort of thing, and another was short circuited because I met the parents long before the dating even began. If memory serves, I met Wendy's parents at her wedding to her ex husband... though I suppose I really wasn't interviewed quite the same way in that circumstance.
The first time I met someone's parents in a more traditional sense we had the issue of religion. They were religious while I am ... not. That sort of thing can be a real strain, especially when you consider the person in the middle who is caught between declaring for either side in that debate. No choice is going to be easy. That said, we pushed through and it was generally fine.
This past weekend was the second 'meet the parents' event (with The Flautist) and religion wasn't an issue this time. However, there is a new issue - polyamory. Specifically, when your daughter says to you "Oh, I am dating a married man now. His wife is totally okay with it, I promise!" there is a certain amount of skepticism that is normal and reasonable.
In my case everyone *is* totally okay with it. It is all open and honest and good.
But even then, if Pinky Pie came home someday with that story I would be suspicious. If it turned out that the relationship did follow that formula I would be perfectly happy with it, but let's face it: There are a lot more married men cheating on their wives than there are poly married men having honest relationships. The numbers do not favour the poly guess, in general.
Most people wouldn't append the story "and I met his wife during my first date with him and we got along great and went to a concert together without him" though, and that certainly adds a lot of credence to the story.
The fact that the people I was meeting had totally valid reasons to doubt my morality gave me some doubt. I didn't figure I would have to cope with accusatory stares and veiled accusations, but these are people I don't know. I wasn't at all sure what would happen.
But it was all good. I chatted with both of them for awhile, talking about work, chores, relationships, and the difficulty of getting paid for creative efforts. Then I had a good ole fashioned debate about energy policy, politics, and voting systems. I am sure that everyone would tell me to stay the hell away from politics when meeting the parents, but since when have I ever backed down from that sort of thing? I did carefully check to make sure nobody was getting upset about the debate, but I really think it was an entirely friendly affair. It helped that we have similar political leanings, though of course we disagreed on the details of implementation.
All in all though it went as well as meeting the parents ever can go, I think. I suppose that generally if people decide that they really need to get along despite having some pretty big differences they can make it work, and that certainly has been my experience so far.