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.