One thing that would worry me about some other cultures is that in some cases they are more bothered about people marrying someone of the same background. My friend had an arranged marriage and the criteria were stupendous (skin tone, caste, religion, education, part of the country she was from etc). I saw how badly her parents would treat someone who didn't meet that criteria and that would worry me for my DCs. I wasn't even allowed to be god-parent for her DD because I was white.
My dad's parents were awful to my mum (she was from a poorer background), so I really appreciate how well I get on with my in-laws. Although their being in a happy relationship is the most important thing, I would be really sad if there were people in their lives making them miserable.
The only other worry I would have, is if they married someone who wasn't a native English speaker there would be more times I would have to explain my DH's terrible jokes, thus making them even more terrible (not offensive, more puns and the like)!
Skin colour, gender, mild religious beliefs that aren't a day-to-day issue - non issues really.