This argument could have been made by any intelligent being, at any point in history, and up to 1500AD or so we have strong evidence that it was wrong every time. If this is the main use of the anthropic argument, then I think we have to conclude that the anthropic argument is wrong and useless.

First, "the anthropic argument" usually refers to the argument that the universe has physical constants and other initial conditions favorable to life, because if it didn't, we wouldn't be here arguing about it.

Second, what you say is true, but someone making the argument already knows this. The anthropic argument says that "people before 1500AD" is clearly not a random sample, but "you, the person now conscious" is a random sample drawn from all of history, although a sample of very small size.

You can dismiss anthropic reasoning along those lines for having too small a sample size, without dismissing the anthropic argument.