I don’t think I have ever seen Obama wear a non-white shirt with a suit and tie. Anyone else seen that? It makes me wonder if a colored dress shirt is not considered formal business wear even now.
It seems to me that colored dress shirts are mostly worn by younger guys. When I wear my suit (usually to church), I almost always wear a colored dress shirt with a coordinating tie (or at least one that doesn’t clash).
It’s not that colored shirts are not business wear; solid white is just the dressiest. It’s most appropriate for certain occasions or situations where you want to look very staid. For instance, when you are the president of the United States, when you have a job interview, when you have a funeral. Most politicians normally wear solid white dress shirts, because almost all of them like a classic staid look.
I wore colored shirts to job interviews and got offers. They were tech firms so maybe that is why.
If I ever wet to another job interview, I probably would not wear a white shirt. But then I might not even wear a tie. (I’m a librarian planning to retire this year.)
And if men went to an event described as “formal”, such as a wedding or a fancy dinner, and they wore a dinner suit with a coloured shirt, I doubt if they’d be turned away. In fact, I suspect some men would wear a business suit rather than hire a dinner suit for the occasion, and I doubt if it would bother most people.
The dress code for the President of a major country is a bit different, because some viewers of his or her costume are likely to be hypo-critical.
This exactly - white is the most formal. Not required IMHO for most job interviews now, except perhaps as a funeral director, maybe a lawyer or banker? Definitely when interviewing to be President of the United States. 
ETA - oddly, as colors go, blue is almost as formal.
Yeah, colored shirts are a step down in formality from white.
In my experience, not a dark blue, but a light one. And some blue dress shirts have white collars and cuffs.
I remember when Regis Philbin was hosting Who Wants To Be a Millionaire?, he introduced me to the idea of wearing a shirt, tie and suit all of the same color, but different shades. Typically, they were all shades of blue.
From what I have seen women don’t dress up much for interviews now - they just wear nice pants and shirt while men still wear suits. Some women may wear a suit but it doesn’t seem to be required now. Again, this is the tech world , I assume it’s still more formal in other industries.
I probably wear a suit once a month or so, for business meetings. I nearly always wear a colored shirt. I’ll note that my client is a pretty conservative group of people (insurance company, located in a small town in the Midwest), and most of them wear colored dress shirts, as well.
The last time I wore a suit and tie was this past Saturday, at a funeral. I wore a white shirt; I felt that it was the most appropriate choice.
Personally, the only non-white shirt I will wear with a suit is light blue, but I’ve seen other guys look good in other non-white shirts. But if there’s too much going on (e.g., striped shirt and a snazzy tie), the guy looks like a suit salesman.