Most of the other answers (including my original one, but maybe not ChrisW's) have accepted your premise that because there is no precise definition of race, any questions about it are unscientific. They have tried to explain how ill-defined questions can be addressed, without simply censoring them.
I want to try a different tack - arguing that lacking a precise definition of race is not a show-stopper.
There is a piece of fallacious sophistry to prove that the colour black is equal to the colour white, that I have seen described several times, but despite searching, I am unable to find a reference (Douglas Hofstatder, perhaps?) which forces me to describe it in more detail than I would like.
Point to something nearby that is black in colour. Now, when you look at it you have to admit it isn't entirely 100% pitch black. It does reflect just a little bit of light. It is really a very, very, very dark grey but no-one objects to describing it as black. Black isn't really one single colour, but a set of very, very dark colours.
In fact, you could add a tiny smidgin more white to the colour, and it would still be black, right? I mean, there is no hard-and-fast rule that very, very, very dark grey counts as black, but very, very dark grey doesn't. Claiming that a particular shade was officially the boundary of black, and even a teensy bit more white made it "not black" would be a ludicrous position to hold on the fuzzy concept of "black".
By simply repeating this exercise, adding tiny bits more white to the colour and demanding that it would be ridiculous to declare that this shade was the boundary, eventually you end up with such a light shade of grey that is, in fact, it is white.
Black is white, logically!
Now such an argument is, itself, invalid. Colours are not rigidly defined concepts, but fuzzy concepts (in the sense of fuzzy logic). The truth value of whether a shade is black can be, for example, "a little bit" or "very".
Nonetheless, colours are useful concepts that can be used and reasoned about with science.
The distinctions between biological species have similar boundary issues, and yet there are many scientific theories based on the concept. Obesity is another.
And so is race. You are right to argue that the boundary definitions of races are difficult to define, and are perhaps even poorly defined in particular studies. You are wrong to suggest that that makes all concepts of race meaningless/unscientific/insidious/racist.
To be clear:
- All individuals belong to exactly one race: False
- Race does not exists as a useful concept: False
- There is no differences in distribution of attributes between races: False
- All differences between races is genetic, as opposed to social/cultural/economic: False
Because people seem to believe these statements are true without evidence, then it is absolutely right that they be discussed on Skeptics.SE.