Your source has more than a few problems.
Firstly, the website itself is not exactly unbiased, but has a very specific agenda.
Regarding the claim that it debunks ... Sorry, I honestly do not find that it does that.
Was there a census based upon ancestry?
What the "debunking" consists of is at best motivated reasoning and speculation. It will no doubt be sufficient to convince those that believe, but really is not robust. There is no ducking the observation that today most critical scholars acknowledge that Luke is not historically accurate.
The claim that Quirinius served two terms is a familiar rebuttal. The flaw there is that the career of Quirinius is well documented and the names and dates of his predecessors are also well documented. The claim, while popular, is not accepted as factual.
