One is that Palestinians are a semitic peoples, while the settlers are nearly all euro-amerikkkan origin. So even by Israel's old testament blood quantum calculus, they have much less claim to the land than the indigenous peoples do.
There are a number of videos that can be found on YouTube displaying reactions from consumers of these kits once their ancestry information is revealed - including one in which an Egyptian-Palestinian figured out that she had Jewish DNA, possibly showing the two cultures are closer in ancestry than they believe.
It’s not actually illegal but it is heavily restricted. Basically no over-the-counter or online purchase kits:
According to the provisions of the Genetic Information Law, genetic tests can only be performed in Israel in medical-genetic laboratories approved by the Ministry of Health according to the conditions specified in the law.
The tweet is also only partially true based on what I can find. It’s not illegal to post the results publicly, but it wouldn’t surprise me if posts like that mysteriously vanished from platforms.
It speaks to the control Israel exerts over its own people and the narrative. It could also speak to their isolationist society and paranoia about being exposed for the massive fraud the country is.