A "white lie" is a small, innocent lie that people tell for social reasons. If I didn't like your mother's cooking, but said I did, it would be a white lie. People often hesitate to give truthful answers about sex--they might tell white lies to protect themselves from embarrassment, even in an anonymous survey. So, there are two different reasons that the question is a bad way to identify sexual orientation. The first reason is that, because the question is about sex, there is a high likelihood that people will give incorrect answers--they will tell white lies. However, even if we assume that the respondents won't lie, a question about past behavior is different from a question about sexual orientation. Some people might have tried homosexual sex and discovered that they didn't enjoy it, or they might have experienced homosexual rape, or they might prefer heterosexual sex but be willing to engage in homosexual sex in unisexual environments like boarding schools, the military, or prison. Other people might desire homosexual sex, but not have had it yet. So, the answer to the question will only be loosely correlated with sexual orientation. It is a bad (aka "wooly") proxy for sexual orientation.

A 'little white lie' is a lie that the person who tells it does not believe to be morally wrong and might try to justify e.g. because it avoids distressing somebody. 'In the absence of' just means 'without'. The writer is therefore saying that splitting people into two groups on the basis of their answer to the question "Have you ever had sex with someone of the same sex?" is a woolly proxy for sexual orientation, even if everyone told the truth. The writer seems to suspect that not everyone did tell the truth