A helpful reminder from You're Not Crazy: "Funny, She Doesn't Look Druish":
Repeat after me: There is no such thing as "looking Jewish." At best, you can describe your bespeckled, big-schnozed, friend with frizzy brown hair as "looking Ashkenazi." But even that's just an ethnic description. Your "-stein" or "-witz" could be a born-Catholic. Appearance and name are totally meaningless when it comes to whether that person is Jewish, either halachically or culturally. And you can't duck the question by saying, "Oh yes, that nice black lady is Jewish, but she must be a convert." She may FFB five generations after an ancestor converted or an FFB of Ethiopian descent. That Indian lady may be b'nei Menashe. That Hispanic guy may be from the (quite large) Jewish community of Mexico City. That Nordic beauty may actually be Hungarian. And yes, maybe any of those is a convert, but maybe so was the parent of your frizzy friendwitz.I will add that this applies in Messianic Jewish circles too. Don't assume that everyone eats matzoh ball soup on Pesach or has a certain look.
The question is pointless and, if anything, one guaranteed to be negative. I know that people think "Oh, you don't look Jewish" is usually intended as a compliment (at least toward a "white" person). In other words, "Oh, you're not as ugly as the rest of us Jews! You look like a shiksa!" Even if it is your intent to compliment, it is wrong to put down the Jewish people in such a way, equating the word "Jew" with "ugly." And it's not even remotely true. So just stop already.
For more on Jewish diversity, see http://bechollashon.org/.