Here are the plot-holes as I see them:
Flaw in your thinking.
You assume that it was available back then.
When I was born, there was very limited genetic testing available and it was incredibly expensive.
More modern versions of it were not available until the early 90's and it took a long time for results and was expensive, and what we see now is less than 10 years old.
Times change and science advances.
"Genome sequencing was once impossibly expensive. The Human Genome Project, an international effort to decode the human genome that launched in 1990, took 13 years and an estimated $2.7 billion to complete. Then, in 2007, DNA pioneer James Watson became the first person to get his genome sequenced for less than $1 million. Since then, the cost of genome sequencing has been decreasing at a rate faster than Moore's law."
If Maria is 23/24 years old at least, as she already has one college degree, using the above figures, it would have cost about $1,000,000 dollars for the orphanage to get her DNA tested.
Because the people of that world hate elves.
WWII Germany, people went from being friendly neighbors to despising their Jewish neighbors, simply because a power mad asshole told them that they were evil, so it is a basic character flaw that some people suffer from.
The elvish rights law is not that old, and the fact that half elves are not covered by it has not been well publicized at all. I believe that they even talk about that, and Marias friend even talks about how she was almost caught up in it and her reasons for not talking about it to even her closest friends, until "AFTER" Maria was taken and she saw how angry they were about it happening.
Only then did she see that she could relatively safely talk about it to them.
So the people who narrowly avoided are not talking about it to save their asses, and the ones that have been caught up in it will likely be beaten for talking about it, and with the sentiments of 83% of the population about how people feel about slaves, most won't give a damn about it anyway, because they are half elf and considered a lower lifeform.