Any problem with simply typing the information? It doesn't seem like it's that hard to type. A year selector just so someone can type four digits seems superfluous.
There are people who are not using A.D. as their calendar year. In this case, it's much less confusing to have a drop down.
If the site is primarily US or EU-based, there won't be much of a problem, but in SEA this is rather problematic since the people usually use their local calendar year when talking about birthday. (For example, in Thailand nobody says "I born in 1986", instead most of us says "I born in 2529".)
(And B.E. is confusing as it is, since there are difference in interpretion between countries, some has year zero and some do not.)